Dynamic Network Visualization1
Dynamic Network Visualization1
James Moody
Ohio State University
Daniel McFarland and Skye Bender-deMoll
Stanford University
Increased interest in longitudinal social networks and the recognition
that visualization fosters theoretical insight create a need for dy-
namic network visualizations, or network “movies.” This article con-
fronts theoretical questions surrounding the temporal representa-
tions of social networks and technical questions about how best to
link network change to changes in the graphical representation. The
authors divide network movies into (1) static flip books, where node
position remains constant but edges cumulate over time, and (2)
dynamic movies, where nodes move as a function of changes in
relations. Flip books are particularly useful in contexts where re-
lations are sparse. For more connected networks, movies are often
more appropriate. Three empirical examples demonstrate the ad-
vantages of different movie styles. A new software program for
creating network movies is discussed in the appendix.
INTRODUCTION
Ranging from simple histograms to dynamic images of the birth of galaxies
(Abel, Bryan, and Norman 2000), visualization tools have always been
key elements in scientific advancement. The ability to see data clearly
creates a capacity for building intuition that is unsurpassed by summary
statistics. Wide ranges of distributional shapes (Handcock and Morris
1 This work was partially supported by grants from the National Science Foundation
(IIS-0080860) and the National Institutes for Health (DA12831, HD41877) awarded
to Moody, and a Research Incentive Award provided by Stanford University’s Office
of Technology and Licensing (grant 2-CDZ-108) to McFarland. Thanks to Mark Hand-
cock, Martina Morris, Walter Powell, Doug White, the participants of James G.
March’s Monday Munch at Stanford University, and participants of the Social Struc-
ture Research Group at Ohio State University. Direct correspondence about this article
to James Moody, 372 Bricker Hall, 190 North Oval Mall, Ohio State University,
Columbus, Ohio 43210. E-mail: Moody.77@sociology.osu.edu
2005 by The University of Chicago. All rights reserved.
0002-9602/2005/11004-0010$10.00
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Dynamic Network Visualization
1999), nonlinear relations, or spatial (geographic or social) proximity can
be easily summarized with an image that helps scientists develop theory.
While the basic principle of substantive clarity is key to successful data
visualization, work in this field is often as much art as science. To build
network visualization tools, we need to examine carefully questions about
the meaning and implication of time in the formation of social networks.
In this article, we hope to extend a bit more science into the art of dynamic
network visualizations and further the theoretical discussion about social
network dynamics.
Social network research has made extensive use of visualization since
Moreno first introduced the sociogram (Brandes, Raab, and Wagner 2001;
Freeman 2000a, 2000b; Freeman, Webster, and Kirke 1998). Actors are
usually represented as points, and relations among actors are represented
by lines, with relational direction indicated by arrows. Early sociograms
were drawn by hand (Whyte 1943; Coleman 1961), and the layout was
determined by the artistic and analytic eye of the author. Such early graphs
were usually simple, having few relations per person or a clear hierarchical
structure.
The state of the art has progressed remarkably since Whyte and Co-
leman, and a growing body of research has developed around various
definitions for optimal network layout (Brandes et al. 2001; Freeman
2000b; McGrath et al. 1997). Most network images do a poor job of
representing change in networks, and researchers make do by presenting
successive snapshots of the network over time (Bearman and Everett 1993;
Powell et al. 2005; Roy 1983). The problem is fundamental to the media.
To effectively display the relational structure of a social network, at least
two dimensions are needed to represent proximity, and that leaves no
effective space (on a printed page) to represent time.2 However, recent
media advances allow us to use space to represent social distance and
movement to represent change over time (Bender-deMoll and McFarland
2002; Freeman 2000b).
2 There have been a number of creative attempts to overcome this limitation, such as
producing multiple images of the network and placing them “next” to each other
temporally (see, e.g., http://www.stanford.edu/group/esrg/siliconvalley/docs/network-
memo.pdf). These approaches require a fair amount of reader training to see the
difference between each plotted time frame. The less-than-intuitive results follow be-
cause these approaches are attempting to replicate a dynamic process in a static me-
dium. Our approach is to use the dynamic nature of such networks directly, thereby
producing a more readily interpretable visualization.
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RESEARCH ON LONGITUDINAL SOCIAL NETWORKS
Much of the recent interest in longitudinal social networks revolves
around understanding how networks develop and change, as scientists
seek to build models of social processes that result in observed structures
(Doreian et al. 1996; Leenders 1996; Nakao and Romney 1993; Snijders
1998; Suitor et al. 1997; Weesie and Flap 1990; Zeggelink et al. 1996).
Such dynamics are important for understanding network stability, which
is necessary for understanding the effect of networks on individual and
group behavior. The clear importance of such questions has prompted a
good deal of methodological research on network change. For example,
Snijders (1996, 1998, 2001) has developed models for evaluating the extent
of change in a social network, conditional on structural features of the
graph.
The purpose of dynamic network visualizations is to help augment
theoretical intuition provided by summary statistics and standard static
visualizations. Until now, visualizations of network change have tended
to take two forms. The first common visualization approach plots network
summary statistics as line graphs over time. For example, Doreian et al.
(1996) present change in reciprocity and transitivity for the Newcomb
data (see also Gould 2002). However, such summary statistics provide
information on a single dimension of a network’s structure. For example,
one might find that a network reaches a given equilibrium transitivity
level, but since transitivity is a single average for the graph as a whole,
we cannot know if this—in itself—means the graph is now relationally
stable. The second common visualization approach is to examine separate
images of the network at each point in time. Unfortunately, such images
are often difficult to interpret, since it is impossible to identify the sequence
linking node position in one frame to position in the next.
THEORETICAL IMPLICATIONS OF NETWORK DYNAMICS
A standing critique of social network research has focused on a “structural
bias” that implicitly denies much of the dynamic nature of social relations
(Emirbayer 1997; Emirbayer and Goodwin 1994). For some types of re-
lations (such as conversations that occur in real time), one could argue
that the networks are largely artificial constructions built by aggregating
dead past events. The network “structure” as such only emerges from this
aggregation. While we do not think this argument should be pushed too
far, it raises important questions about how the temporal embeddedness
of relations defines a dynamic social space. While discussions of meaning
and temporal abstraction in themselves are not new (Abbott 1997; Bear-
man et al. 1999; Danto 1985), our goal is to identify a meaningful way
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to capture network dynamics empirically that simultaneously allows for
the importance of past relations typically captured in static network
images.
Basic Terms
Much research on social networks is filled with static nouns, such as
“roles,” “relations,” “obligations,” and so forth. Longitudinal research on
social networks requires a different set of process terms, such as “ritual,”
“dance,” “pulse,” “tempo,” “congealing,” or “dispersal.” The key distinction
is that an apparently static network pattern often emerges through a set
of temporal interactions, with important implications for the relational
process under investigation. For example, when viewed in continuous
time, networks may develop by spurts or build slowly and steadily, or
they may reflect repeated ritual behaviors that mix moments of order and
chaos.
The most basic dimension for dynamic relations is relational pace.
These are questions concerning the rate of change in relations, with par-
ticular interest in irregularities. The pace of relation formation can thus
be described with respect to levels (fast, slow), change (accelerating, de-
celerating), or stability (cascades, jumps and starts, etc.). Clearly, the exact
meaning of such terms depends on context, since the relevant scale will
vary across types of relations. Think, for example, of seconds for con-
versation networks, weeks for friendship networks, decades for world
trade networks, and generations for kinship networks (Nadel 1955; Collins
1981).
A second specifically temporal aspect of relations revolves around the
order of relations, or their sequence. In many circumstances, being able
to explain the prevalence of given structures depends on identifying the
order in which relations occur. For example, the distinguishing charac-
teristics of Johnsen’s (1985, 1986) process agreement models for friendship
formation depend on whether one first forms reciprocal friends, which
then generates agreement on third parties and creates transitive ties, or
if two people first agree on their admiration of a third, which draws them
together in friendship. Similarly, Chase’s (1980) explanation for the de-
velopment of hierarchy in social relations rests on a particular order of
relationship unfolding.
A special case of the intersection of pace and sequence is found in
notions of concurrency developed for disease networks (Kretzschmar and
Morris 1996; Morris 1993). Two relations are concurrent if they overlap
in time and share at least one person. While static views of networks
focus on multiplicity (the overlap of types of relations), concurrency is
effectively “temporal multiplicity,” which can dramatically complicate our
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American Journal of Sociology
understanding of relations. Moody (2002) shows that the temporal un-
folding of relations reduces reachability, which has implications for any
measures on networks with relations enacted in real time. Consider, for
example, the different disease implications of a relational “switching”
model, where actors retain past relations until they are secure in new
relations, leading to a sequence of short-duration overlaps and a multiple
partner model, where people overlap for extended periods of time with
multiple partners (Laumann and Youm 1999).
Finally, the richness of a relational structure further expands when we
link relational timing to types of tie. When we allow simultaneous con-
sideration of the pace and sequence of ties with variation across types of
ties, we can start to tap questions of how sets of interaction sequences
transform into stable relations (see Nadel 1955). For example, if theoretical
discussions of local action (Leifer 1988; Padgett and Ansell 1993) are
correct, then we should be able to map social interaction as a sequence
of seemingly random “milling around” that quickly cascades once role
positions are fixed. This type of rich network visualization provides a
more holistic understanding of the network’s structure than any single-
dimensional index could.
These are just a small number of the theoretical considerations evident
when one takes time seriously in the modeling and understanding of social
networks, and we expect that others will contribute much to this discus-
sion. Our belief is that any such discussions are best grounded in empirical
investigation (Abbott 2000), which will be enhanced with a set of flexible
tools for displaying dynamic network data.
REPRESENTING LONGITUDINAL NETWORK DATA
To develop dynamic network images, we need to conceptualize clearly
how time is encoded in social networks. We conceive of time in two
analytically distinct forms: discrete and continuous. Discrete renditions
of time consist of cross-sectional snapshots of the network. Hence, lon-
gitudinal analysis focuses on the change from one network state to another
without any (explicit) reference to the sequence of changes that generate
change. In such cases, a process is generally inferred from the total net-
work change across time. Due to research costs and design, most longi-
tudinal network studies use discrete time. Continuous renditions of time
consist of streaming relational events or interactions recorded with exact
starting and ending times. Streaming relational events consist of sequential
dyadic events or interactions whose visual representation should unfold
as a continuous social process. Continuous representations of time enable
researchers to identify how overall network changes emerge through or-
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dered dyadic events. But, researchers need not analyze the data in its
most reductive form, as they can aggregate relational events into larger
time units (such as minutes instead of seconds). Hence, it is possible to
develop discrete notions of time from continuous data but not vice versa.
If researchers have many panels of network data or continuous rep-
resentations of network change, they have several decisions to make before
they represent the data visually. First, what constitutes their networks?
With discrete waves of sociometric surveys, each wave becomes the net-
work used in graphic representation. However, with continuous data it
becomes more difficult to define a network’s temporal boundary (Lau-
mann, Marsden, and Prensky 1983).3 Is the network defined by 10 rela-
tional events, all the events in one minute, in 10 minutes, or in a single
day? The answer to this may depend on the empirical focus of the re-
searcher, but what is undeniable is that we cannot select each dyadic
event as a network. A network consists of a pattern of social relations,
and therefore we must identify chunks of time that substantively capture
the nature of relational events and the character of temporary networks
that arise in the focal context.4
For visualizing continuous network data, we characterize a network
by a time window that spans a set of relational events (Bender-deMoll
and McFarland 2002). The relational events that transpire within a win-
3 One could argue that Laumann et al.’s (1983) discussion of nominal and realist notions
of networks’ spatial boundaries also applies to networks’ temporal boundaries. Realist
notions of time will have natural boundaries that actors acknowledge and recognize
(i.e., school weeks and days, class periods, etc.). Nominalist notions of time boundaries
are defined by the researcher for a variety of theoretical concerns (i.e., development
focus, period of historical change, etc.).
4 There is a conceptual tension here regarding what a network consists of and how
different kinds of representations will offer different understandings of network change.
This is a conceptual issue that runs to the heart of network theory. The general
structuralist view is that relations form from repeated interactions and their aggregate
patterns (Nadel 1955; Hinde 1971). In contrast, interactionists argue that relations and
roles are established by ritual patterns of interaction that have a particular sequence,
such that reordering the sequence of interactions would undermine the meaning of the
ritual and relation being enacted (Goffman 1967). Work in social movements and
collective action suggest that it is not so much the accrual of everyday interactions
that constitutes a relation but the rare, jarring events which lock in or rewire relational
patterns (Gould 1995). Finally, work on diffusion treats relations as conduits for the
transferal of goods, and relational timing acts as a “switch” determining temporally
“downstream” nodes from “upstream” nodes (Moody 2002; Morris and Kretzschmar
1997). Regardless of the outlook, a more fine-grained perspective may reveal change
processes in more substantive detail. From the study of continuous relational events,
we may learn how ordered dyadic acts can form ritual patterns emblematic of roles
and relations (enriching the aggregate interaction view to include order), and how rare
jarring events reverberate through relational structures so as to create network change,
or how the unfolding of relations creates diffusion opportunities (Emirbayer 1997;
Emirbayer and Goodwin 1994; McFarland and Bender-deMoll 2003).
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dow of time are aggregated into a network. One implication of the time
window is that relational events have a residue that extends beyond their
occurrence, defined by the length of the time window. For example, in
the classroom data discussed below we have streaming interactions spec-
ifiable to seconds. Since many interactions take hold of actors’ attention
for a short time after they occur (at least), we decided to make the time
window equal to 2.5 minutes, which affords a relatively meaningful graph
for characterizing the interaction pattern arising in that class (see fig. 1).
The “time window” defines a right open interval (from “slice start” to
“slice end”). Events that fall inside the interval (arcs 2–5, node C) or
ongoing events that extend past the interval’s bounds (nodes A, B) are
included in the network. This method is quite flexible as it deals fairly
well with the aggregation of both “instantaneous” events and those having
a defined duration. Successive networks are generated by incrementing
the values for “slice start” and “slice end” points by a constant (delta)
value.
After we define the window of time, the next decision is whether suc-
cessively defined windows are to be overlapping or nonoverlapping.5 For
example, if we aggregate streaming dyadic relations into 2.5 minutes of
class time for defining the network, we can make the next window consist
of the next 2.5 minutes (nonoverlapping) or have it partially overlap with
the current one, as in a moving average (see Doreian 1980, 1986). The
most incremental relational change consists of a new window that only
has one tie added to the front of it and another dropped off the back.
The third set of concerns center on the timing of arc representation.
The placement of nodes in a graph is distinct from the animation of a
particular relation. One can use the network data to generate coordinates
for nodes and then control the animation of when relations are shown by
a different procedure. We have found that the timing of arc representation
helps viewers see the network process more clearly because it clarifies the
link between relational change and node placement. In essence, the an-
imation of arcs follows a second time window, a “render window” that
“slides” from one network time window to the next. Nodes and arcs are
drawn and deleted as the render moves over them, and the node coor-
dinates are adjusted incrementally between the two layouts (see fig. 2).
The process of creating a visual transition from one network’s layout
coordinates to another involves drawing a number of intermediate “ren-
ders” of the network while gradually adjusting node coordinates and
adding or deleting nodes and arcs as they fall within the moving render
window. Successive network windows may overlap, which is controlled
5 In SoNIA, we define the degree of overlap by a delta measure, which indicates how
much time is added or subtracted from the prior window.
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Fig. 1.—Construction of a “network slice” by binning node and arc events
by the relationship between the duration of the time slice window and
the offset between successive windows (bin delta).
If the network data are continuous, adjusting the size of the render
window in relation to the network window allows the researcher limited
control over how many new relations tend to lead or lag node movement.
For example, A’s interaction with B can lead nodal position such that
the arc transpires and then the nodes shift position; or we can lag inter-
action such that nodes move closer to one another and then an arc forms
(as if nodes first draw near each other and then talk). However, the actual
timing of arc representation is determined by where an arc’s time coor-
dinates land relative to those of the bin.
NETWORK VISUALIZATION
Graph Layout Principles
Good reviews of the history of network visualization can be found in the
literature (Freeman 2000b). The effectiveness of network visualization
technique differs by network size. Small networks can focus on detailed
elements of the graph structure while larger networks can mainly capture
gross topology. Visualizing networks of tens of thousands of nodes requires
further abstraction yet.6 Our interest in this article is identifying layout
principles that are useful for research in small to moderate sized networks
(fewer than about 100 people).
A useful goal for most social network layouts is to represent social
6 See app. B (online only) in this article for a static example and Powell et al. (2005)
for a dynamic example.
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American Journal of Sociology
Fig. 2.—Transitioning between slices with a sliding “render window”
distance as physical distance.7 This representation allows viewers to get
a spatial understanding of social relations, as nodes with many relations
in common are placed close together on the printed page. An intuitive
impression of the network structure then emerges from the proximities in
the image. For example, one can easily see racial segregation in a network
image as the clustering of races into distinct spaces on the page (Moody
2001b, p. 683). A social-distance-based representation of network structure
is facilitated when edge lengths are equated to relational strengths. Various
force-directed layout techniques are usually successful at this.8
Within the larger topology, aesthetic features of the graph help facilitate
readability. All else equal, edge crossing, running edges “under” nodes that
are not connected to each other, and stacking nodes on top of each other
7 For this article, social distance is defined graph theoretically as the length of the
shortest path in the network connecting two nodes. However, alternate formulations
might be interesting and advisable depending on a researcher’s theoretical framework.
8 There is a difficulty here when ties are directed, since the visual distance from i to
j has to equal the visual distance from j to i, even though social distance need not be
symmetric. In SoNIA, we use the basic correspondence between screen distance and
social distance to evaluate layout fit, using a modification of Kruskall’s stress measure,
2
(ScreenDist
GraphDist)
ij
Stress p
,
2
GraphDist
ij
where ScreenDist is the Euclidean distance of the layout x–y coordinates, and
GraphDist is the geodesic distance based on an underlying symmetric graph.
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all hinder readability of the graph (Davidson and Harel 1996). While we
do not explicitly control these features in the movies below, they are key
elements in our evaluation of the resulting graph layouts. Color, size, and
shape are useful ways to add additional information on actor or relational
attributes. We have found that visualizing multiplex ties—multiple ties
of different types—can be effectively represented with colors and “trans-
parent” arcs, which allow you to look through the edge to see multiple
relations on a single dyad as a blend of colors.
Graph Layout Algorithms
Force-directed or spring-embedder algorithms are among the most com-
mon automatic network layout strategies. These algorithms function sub-
stantively on an analogy, treating the collection of nodes and arcs as a
system of forces, and the layout as an “equilibrium state” of the system.
Generally, edges between nodes are represented as an attractive force (a
“spring” pulling them together), while nodes that do not share a tie are
pushed apart by some constraint to help prevent overlap. The two most
common layout algorithms are Kamada Kawai (KK; Kamada and Kawai
1989) and Fruchterman Reingold (FR; Fruchterman and Reingold 1991).
For FR, the underlying model roughly corresponds to one of electrostatic
attraction in which the attractive force between connected nodes is bal-
anced by a repulsive force between all nodes. For KK, it is as if all nodes
are connected by springs with a resting length proportional to the shortest-
path distance between them. For both KK and FR, the relations between
nodes must be expressed as distances rather than adjacencies. In KK, this
“dissimilarity” matrix is constructed from geodesic distances between
nodes. In FR, the dissimilarity matrix is constructed directly from
adjacencies.
Both of these algorithms are available in current network drawing
software, such as Pajek (Batagelj and Mrvar 2001) and NetMiner (Cyram
2003). The algorithms work by iterative optimization—adjusting a node’s
position by reacting to the positions of others. As such, the starting position
of the network affects the outcome. The details of the optimization pro-
cedure can also affect layout. Because there are no exact calculations of
global minima, layouts are subject to local convergence problems.
A second class of algorithms plots nodes using the dimensions that result
from multidimensional scaling (MDS) techniques based on the geodesic
distances or some alternate measure of node similarities.9 These layouts
are available in common software packages, such as NetDraw, Krackplot,
or MultiNet. Substantively, metric MDS models reduce the n
1 dimen-
9 Technically, KK could be considered a variant of nonmetric MDS.
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American Journal of Sociology
sions present in a network to the two dimensions that capture most of
the variance in observed multidimensional distance. Because they take
input distances as their starting point, these models do not, in themselves,
attempt to stop nodes from stacking on top of each other, and as such
they can easily generate layouts where structurally equivalent nodes oc-
cupy the same location. Many authors correct for this by adding a small
amount of noise or other correction to the resulting structure. One the-
oretical value to the metric MDS model is the direct linkage between
input relational distances and resulting display. Nonmetric MDS algo-
rithms use one of a number of optimization techniques to find a “low-
stress” (well-balanced relation between input and screen distances) layout.
Because of the necessity of giving results in terms of two-dimensional
distance, both force-directed and MDS models are symmetric, using either
a symmetric input distance matrix (MDS) or having symmetric forces
driving/pulling nodes together in force-directed layouts. While the dis-
tinction between direction and distance is irrelevant in static layouts, it
can be substantively important for dynamic layouts, as we often want
nodes to follow their nominations. To accommodate direction, we intro-
duce an algorithm that follows a simple peer influence analogy, building
on a suggestion in Moody (2001a). A node’s position is a function of their
prior position based on a self-weight and the average position of those
they nominate (see fig. 3).
In figure 3, the thin black arrows indicate nominations, while the wider
gray arrows indicate net force for each person’s movement. Person 2
should move down in response to the force of ties sent to persons 1 and
3, while 3 moves slightly to the right based on the net pull of 4 and 5
over the pull of 2, and slightly up as a function of the net pull of 2 and
4 over 5. Similarly, node 6 moves toward the center of nodes 1, 3, and 5,
based on the strong difference in their positions. It is important to note
that nodes 1, 4, and 5 should not move at all, since they send no ties
elsewhere in the network.
The peer influence algorithm works by computing the weighted average
of a node’s current x and y positions and that of those that node nominates.
This process is iterative, adjusting each node’s position to that of others
multiple times.10 As with the metric MDS layouts described above, the
algorithm makes no explicit reference to resulting node positions, which
can result in nodes stacked on top of each other. The result is often similar
in flavor to a metric MDS plot, which should not be surprising given their
10 In practice, the number of needed iterations is quite small, as the procedure tends
toward high “consensus” positions. Similarly, high self-weights generate more stable
movies.
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Fig. 3.—An example of the peer influence layout algorithm
common roots (under a particular set of assumptions) to a general class
of eigenvalue models (Friedkin 1998).
EMERGING NETWORKS
In many settings, the substantive question is the emergence of a cumu-
lative network structure. Relations in such settings are temporally sparse,
requiring the aggregation of many periods (i.e., a large time window) to
generate a meaningful image of the network structure. For example, a
high school romantic network viewed on any given day will consist largely
of a set of completely disconnected dyads, since only a small number of
students are involved in multiple romantic relations on any given day.
Viewed contemporaneously, this network is essentially structureless. How-
ever, sexually transmitted disease risk resides in the history of previous
relations, which cumulate and thus provide pathways for disease trans-
mission. As such, we are substantively interested in both the cumulative
structure of the network and the process through which the structure
unfolds.
We have found that one of the most effective ways for displaying such
sparse networks is to show how the network emerges over time, by adding
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nodes and relations as they appear, but placing them in the display plane
based on the final aggregate structure. The dynamic element then appears
by revealing the network over time and seeing the pieces grow together.
As new nodes and relations enter the population, they are added to the
graph. To effectively distinguish current relations from past relations, we
“ghost” relations when they end (i.e., fade out).
As an example, consider the graph given in figure 4 below, which is a
small section of the sociology collaboration network (Moody 2003), re-
cording all article collaborations (among this small sample) between 1963
and 1999. Based only on the image in figure 4, it appears clear that node
A is at the center of this network.
However, our impression of this network changes if we examine how
it develops over time, as can be seen in movie 1. (All movies in this article
may be viewed in the online copy of AJS.) Here we see that the relations
connecting the full component only form much later in the unfolding of
the network. Note also that the pace of relations is evident in the movie,
as the structure admits to a four-year “dormant” period between 1969 and
1973 when no changes occur. One’s understanding of the betweenness of
these center nodes changes once the temporal nature of the network is
revealed.
As a second example, consider relations among all people in the largest
connected component of an adolescent romantic network (see Bearman,
Moody, and Stovel [2004] for details of this structure’s development;
Moody [2002] for a discussion of dynamic diffusion implications). Figure
6 shows all relations that were active in the 18 months prior to the
interview.
The most striking feature of the static network is a large connected
component, linking 288 students through romantic involvement. When
viewed dynamically, we see that this structure emerges quite late in the
local history of the network and is never observed as a complete structure
at any point in time. Moreover, a close review of the movie reveals that
certain contemporaneous substructures never occur—namely four-cycles.
Prior work suggests that avoiding such four-cycles helps generate the
sparse treelike structure of the network (Bearman et al. 2004). In general,
this flip book approach is among the simplest network movies to imple-
ment. The technique will likely be most effective when one is interested
in the cumulative graph structure, or when one can meaningfully fix node
position in an x-y space.
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Fig. 4.—Sociology coauthor selection; nodes colored by sex, size proportional to degree
DYNAMIC NETWORK MOVIES
Perhaps the theoretically most promising advance for dynamic network
visualization lies in using node movement to map changes in the under-
lying network structure. Substantively we are often interested in endog-
enous network processes. Examples include identifying how conversations
build in classrooms to transform an ordered teaching environment into a
cacophonous menagerie, the development of powerful positions through
business exchange, or the endogenous emergence of social structure from
actor-based interaction rules. In all of these cases, we suspect that the
structure at time t influences the structure at time t
1 in systematic
ways, and being able to visualize the transformation of the structure can
help identify the mechanisms through which such changes occur (Mc-
Farland and Bender-deMoll 2003).
Requirements for Meaningful Dynamic Layouts
All of the aesthetic requirements for static graphs apply to dynamic
graphs. In addition, however, a number of factors are unique to dynamic
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Movie 1.—Online
representations that need to be addressed. An animation or interpolation
technique is needed to create meaningful movement between temporally
adjacent network slices. Most useful for this is a sinosodal animation
technique that gradually interpolates the position of a node from one
resting position to the next. This interpolation is what helps the eye follow
changes in the graph structure over time.
Given the ability to animate change in the network structure, one must
then assure that the layout at time t
1 is linked to the layout at time t
to avoid meaningless movement in the graph. While simple on its face,
the separate application of standard layout algorithms to each time slice
will rarely give a satisfactory result. Instead, as network layouts usually
have no inherent coordinate axes, the entire graph tends to “rotate” and
“flip” in the display space. A partial solution to the problem of spurious
movement rests in developing an adequate starting position or “anchor”
for the network that results in a meaningful orientation for the graph.
The anchor choice is not theoretically neutral, as it will affect the resulting
layout. Below we identify multiple anchor possibilities and discuss the
implication of each.
In addition to providing meaningful movement linked to relational
change, a number of additional features of nodes and relations should be
temporally variable as well. A successful layout should be able to accom-
modate changes in relational strength, type, and valence (expressed as
edge attributes), as well as changes in node attributes (expressed as shape,
color, and size of nodes), so that temporal changes in attributes will also
be apparent. Finally, while static graphs are usually agnostic with respect
to relational direction, in a dynamic setting we might want to distinguish
movement based on tie direction.
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Movie 2.—Online
Anchoring Temporal Networks
The first layout possibility is really not an anchor but the use of random
starting positions, which we term “random anchoring.” Points are initially
distributed randomly throughout the x-y plane, and the algorithm uses
these initial starting positions. In general, a random anchoring is effective
only for determining the initial (time 1) layout, and using a new random
set of starting coordinates at each observed time point usually results in
meaningless motion. However, one can test (qualitatively at least) the
effect of starting position on eventual layout by running the same figure
multiple times with new starting values.
Alternatively, one can use a constant fixed position as the starting an-
chor for all times, resulting in a “fixed anchor.” The most common such
anchor might be a simple circle. A second common starting point would
be based on some function of the overall graph structure. For example,
one might build a cumulative graph as the sum of all interaction over
the observation period and generate initial layout positions from this
aggregate graph. Or, one might use a meaningful nonrelational distance
metric for the starting conditions, such as the latitude and longitude of
cities in a trade network or the seating chart in a classroom network.
In any such fixed anchor case, movement from time 1 to time 2 reflects
differences in the structure of relations between time 1 and time 2, since
starting positions are “held constant” across graph observations, which
greatly reduces superfluous movement. Substantively, using the circle as
a fixed start point can result in systematic distortion in the overall display
fit (if, e.g., nodes that are often connected to each other are placed on
opposite sides of the starting circle), though movement will still be con-
sistently related to graph changes. Using an aggregate graph layout po-
sition can sometimes lend a bit more consistency, as each observation
window starts “near” the bulk of the structure observed for the whole
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period. In practice, we have found these types of starting values most
effective for the metric MDS and peer influence algorithms.
Finally, an obvious anchor for a network layout at time t is the graph
layout at time t
.
1 We term this a “chaining anchor,” and it fits well,
substantively, with our intuitive notion of a network movie, as we are
literally plotting the change in node position from time t to time t
1.
Substantively, this model uses only the information embedded in prior
positions for graph layout. As we show below, the chaining anchor seems
to work best with force-directed layout algorithms, particularly when
network change is small, as starting from t
1 coordinates helps the
algorithm find an optima at t that is geometrically close. But when used
with the metric MDS or peer influence algorithms, we often see a network
“inertia” effect, where nodes quickly converge on a very small portion of
the total display space, resulting in a largely unreadable movie.
MOVIE EXEMPLARS
Data
In the examples that follow, we use data from three sources chosen to
reflect a wide range of potential applications, moving from theoretical a
priori simulations, to a well-known classical dynamic network, and finally
to complex, multiple relations, streaming interaction data within class-
rooms. Below we first describe the three data sources and then describe
the dynamic movies for each.
Simulating Social Balance
Social balance theory encapsulates the folk notion that “a friend of a
friend is a friend,” suggesting that people avoid friendships where their
friends are not friends with each other and form friendships when others
relink the pair. Primarily a theory of relational change, social balance
theory is a clear candidate for exploration with dynamic tools. The es-
sential prediction of much of the work on balance theory is that through
a relational adjustment process, ordered social structure can emerge en-
tirely endogenously (Davis 1963, 1970; Davis and Leinhardt 1972; Doreian
et al. 1996; Johnsen 1985). Part of the power of this model rests in the
understanding that global implications follow from local relational action.
The simulation starts with a simple random network of 45 actors who
each nominate (on average) four other people. At each of 200 iterations,
five randomly chosen nodes evaluate their local network with respect to
transitivity, intransitivity, and reciprocity; nominations are changed if do-
ing so increases the comfort of the actors’ overall position with respect
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to these characteristics. Actors favor relations that are transitive, avoid
those that are intransitive, seek to reciprocate nominations, and avoid
making long-term asymmetric nominations (Gould 2002). In addition,
actors have a small preference for current ties over changing ties and do
not have perfect vision, but instead evaluate the returns to changes in
their local network with a small amount of random error.11 This model
is useful for demonstrating the endogenous emergence of order from ran-
domness and demonstrates how seemingly stable summary statistics on
one network dimension can mask significant structural change on other
dimensions, highlighting the holistic-view payoff to this technique. For
the purposes of the movie, we sample the network at every other iteration,
resulting in 100 discrete images of the network.
Newcomb Fraternity
Newcomb’s fraternity is among the best-known dynamic data sets in
common usage. We use a version of this data that comes standard with
UCINET (Borgatti et al. 1999). The data consists of each student pro-
viding friendship rankings for every other student in the fraternity. Fol-
lowing Doreian et al. (1996), we recode the original rank data so that the
top four positive ties are retained as “friends,” but use the original rank
data for summary transitivity measures. These data provide a real-world
complement to questions of social balance raised in the simulation above.
McFarland Classrooms
A third data set stems from McFarland’s repeated observations of social
interactions in over 150 high school classrooms during the 1996–97 school
year. We show dynamic network representations of social interaction from
two of these classes below. The first class (class 173) is an accelerated
trigonometry class at a magnet high school. It is composed of tenth graders
who are tightly controlled by an authoritarian male teacher. The second
class (class 182) is an honors algebra 2 class at the same magnet high
school. It is composed of mostly tenth graders (light gray), but also a few
eleventh graders (dark gray), and it is taught by a progressive but bum-
bling male teacher (McFarland 2001).
The data on classroom interactions consists of streaming observations
of conversation turns. The conversation turns were recorded as pairs of
senders and receivers and for types of content. Speakers were viewed as
directing their communication in one of two fashions: (1) indirect sound-
11 The simulation is implemented in SAS IML (interactive matrix language) and is
available from the first author.
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ings, such as lectures (where a teacher addresses all students); and (2)
direct interactions that are focused on particular others. Each type of
directional speech is viewed as having different forms of network recep-
tion—indirect speech reaches all bystanders as passive hearers, and di-
rected speech reaches the focal person as an active coauthor of the con-
versation (Goffman 1981).
Two types of interaction are found to prevail in classroom contexts:
task and sociable (McFarland 2003). Task interactions are those behaviors
that pertain to the ongoing teacher-prescribed task (content is academic).
In contrast, sociable interactions concern everyday concerns of adoles-
cents’ social lives, such as parties, dating, social outings, plans, and so
on. While the content is the key distinction, it is often the case that these
speech acts are distinguishable in style as well, where sociable behaviors
are more playlike, fast paced, and free than the more constrained academic
styles of speech during lessons (Cazden 1988). Last, observations also
recorded when task and sociable forms of interaction were laminated with
evaluative meaning. Such evaluations were seen as being either positive
or negative—either giving praise or attempting a reprimand (Ridgeway
and Johnson 1990).12
RESULTS
Example 1: Dynamic Order from Randomness
Our first example is of the simulated balance process. Figure 5 presents
summary statistics over time, including the reciprocity and transitivity
rates and the proportion of arcs that change from iteration to iteration.
Balance theory predicts that people should adjust their relations until
they reach largely consonant friendship groups, at which point the net-
work should stabilize around a pattern where everyone’s ties are (largely)
transitive. The simulation summary evident in figure 5 suggests this is
essentially the case, as transitivity rises steadily for the first 100 iterations
or so, then largely stabilizes after that. Reciprocity quickly rises early in
the simulation, then falls briefly (around iteration 20), then continues to
12 This coding method was piloted in two prior studies by McFarland (2001) and had
a high degree of accuracy in more teacher-centered classroom lessons due to the turn-
taking sequential nature of discourse. In more chaotic classrooms, simultaneous turns
at talk often prevented the observer from acquiring perfect accuracy. However, some
record was made of when such diminished accuracy was acquired. The two class
periods used in this paper were considered to have a high degree of accuracy in their
coding. For the movies included below, we use 2.5-minute moving windows that
overlap in incremental shifts of 0.5 minutes. We believe this method best captures the
fluidity of interaction patterns but diminishes the amount of artificial fluctuation across
frames so that some continuity is had.
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Fig. 5.—Reciprocity and transitivity in a dynamic balance simulation
rise steadily throughout the simulation.13 Movie 3 presents a dynamic
visualization of this simulation. In this figure, blue ties represent asym-
metric nominations and green ties represent symmetric relations.
The movie shows the emergence of structure out of randomness. The
initial stages of the movie show very little structure. Instead, actors are
simply “milling around”—as they adjust relations in response to the initial
random tie allocation. After about 50 iterations, two patterns emerge.
First, a set of initial “protogroups” forms around four-person cliques.
These small protogroups form the structural kernels that future relations
orient around as time progresses. Second, a small number of “stars”—
people receiving a relatively large number of asymmetric ties—become
evident. Star status proves somewhat unstable, however, as the search
for reciprocity means that nodes only nominate stars for a short time.
However, as a counterforce, the push for transitivity means that connected
pairs will nominate thirds in concert, resulting in a continuous existence
of stars in the setting. About halfway through the simulation, it becomes
13 The network movie provides a nice explanation for this pattern. The drop in reci-
procity seems to occur because the initial rise in reciprocity leads to a large number
of intransitive triads. As the number of intransitive triads increases, the transitivity-
seeking pressure seems to overpower reciprocity seeking, and adjustments are made
to build transitive ties, and then within the transitive sets, reciprocity increases. This
pattern is consistent with theoretical and empirical expectations on real networks
(Sorensen and Hallinan 1976).
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Movie 3.—Online
clear that the network is no longer a purely random collection of nodes,
but instead a loose federation of groups weakly connected through asym-
metric ties. At this point, the group-group structure becomes interesting,
as high-degree actors change asymmetric ties between groups, changing
the relative links of groups to the remaining network. Here we see the
component structure change, as groups break away from each other into
smaller collections.
Throughout the remainder of the movie, the structure never crystallizes,
but instead “bubbles” as nodes form links between different groups. Nodes
make nominations to others in the setting that are then built on by others
in response to the changing conditions. The resulting temporal network
story, then, becomes one of changes building on change, and a group-
level dance that emerges as some group members form ties to others. That
some of these changes are, surely, the result of the random component
built into the simulation is less interesting than the fact that such random
events can have systematic effects in the structuring of others’ responses.
While not intended to model any particular real setting, the image one
gets from the resulting movie might well mirror the development of con-
versation groups in a cocktail party, as sets of people mingle and even-
tually find those they wish to speak with on a more engaging basis. The
simulation also fits well with recent work on the systematic effects of a
small number of random ties (Newman 2000; Watts and Strogatz 1998).
Technically, we consider this a successful visualization because almost
all of the movement evident in the graph results directly from interpretable
changes in underlying network structure. The visualization used the KK
layout algorithm and a chain-based anchor. (For alternative movies using
different layout algorithms, see app. B).
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Example 2: Multiple Visions of Newcomb’s Fraternity
The substantive story usually told about Newcomb’s fraternity is one of
structural convergence as a group of new college students meet and form
friendships (Doreian et al. 1996; Newcomb 1961; White et al. 1976). This
description of the data rests on evaluations of summary measures (or
aggregate blockmodels) of the network. However, the “convergence” story
of the Newcomb data is not uncontroversial since up to 20% of the ties
change even in the last few weeks of observation. Finding local fluidity
and global stability (as measured in blocks or summary statistics) suggests
that change moves through structurally equivalent actors. Figure 6 plots
the reciprocity and transitivity rate over the 15 observations.
Figure 6 plots the change in reciprocity and transitivity, using the coding
scheme described in Doreian et al. (1996). The figure suggests, and many
have interpreted these data as showing, that the network reached a par-
ticular level of reciprocity early, while transitivity increased throughout
the 15-week observation period. However, when combined with the arc
change information, one could argue that reciprocity never converges in
any meaningful sense but instead fluctuates substantially over the entire
observation period. Similarly, transitivity increases steadily, and the
change is more than you would expect by chance (Doreian et al. 1996,
p.124), but the degree of change is not dramatic (moving from 0.75 to
0.80).14 How does our image of the Newcomb data differ when we view
changes in the entire network simultaneously? In the movies that follow,
reciprocated nominations are colored green and given a width equal to
the average of the two arcs. Asymmetric ties are blue, with width equal
to the strength of the nomination.
Movie 4 presents a KK algorithmic chain-anchor layout version of the
Newcomb fraternity network, matching the version used in the balance
simulation above. The first impression of this movie is that the network
seems to change a great deal over time. This is partially due to the fact
that, unlike the simulation example, the Newcomb data were collected
in discrete waves, so there are large numbers of edge changes between
subsequent networks. Close examination suggests that many nodes are
moving even when their relational ties do not change (though the ties of
the people they are tied to change, and thus the whole system should
change shape). Some of this movement, however, seems excessive and
hard to follow. Consider instead movie 5, which uses the FR layout
algorithm.
Movement in movie 5 is more subdued, and the pattern of interaction
is somewhat easier to follow. For example, one can see that nodes 1, 6,
14 The transitivity measure used here is based on a sorted rank model.
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Fig. 6.—Reciprocity, transitivity, and change in Newcomb’s fraternity
8, and 13 remain strongly connected to each other throughout the obser-
vation period, occupying a small cluster at the right of the graph. Nodes
7, 12, and 4 form a cluster early in the group’s history, but node 4 then
breaks with this group at about week 8, instead nominating nodes 17 and
2. In general, there is still a great deal of movement in this graph, and
the large number of asymmetric ties suggests that we might gain some
insight by using a layout method that accounts for this asymmetry.
Movie 6 uses the peer-influence layout algorithm, with a cumulative
graph anchor (the starting position is based on a KK layout of the average
positive tie value between every pair cumulated over the entire obser-
vation period). Here we immediately see a quick break between those
embedded in largely symmetric relations and those hanging on to the edge
of the structure. Nodes 10 and 15, for example, quickly emerge as nodes
on the edge of the social structure. While they nominate each other sym-
metrically early in the observation period, they lose interest in each other
by the end. Neither node receives top-five nominations from any other
node in the network. Their nominations to others seem to dance around
the graph, never resting for long on a single person. The group-structure
dynamics also become clearer, as node 17 seems to be a popular actor
bridging the cluster formed around nodes 1, 6, 8, and 13 and a smaller
(and less stable) cluster surrounding nodes 7 and 4.
Hence, the movies suggest that the overall structure does not converge
on a single form, and that the process of change is heterogeneous, with
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Movie 4.—Online
some actors forming stable relations while others dance between friends
throughout the observation period. This insight suggests disaggregating
the network change statistics evident in figure 6, which we do in figure
7.
Figure 7 presents the results of a cluster analysis on the sequence of
network change scores (calculated as the correlation between each per-
son’s time t and time t
1 nomination vector, to retain the full range of
rank data). A three-cluster solution is instructive. Two groups follow a
simple convergence story, with their nominations getting progressively
more stable as time passes. The first of these groups (group 1 in fig. 7)
has seven members, including the cluster at the right of the movie (1, 6,
13, 8), and presents a gradual convergence of nomination patterns, while
the second (group 2, with six members) does not converge on stable nom-
ination patterns until week 5. Finally, group 3 (with four members, in-
cluding the hanger-on nodes 10 and 15) never seems to settle on a par-
ticular nomination pattern, but changes nominations steadily over the
observation period.
The substantive advantage of the dynamic movie, in this case, is to
identify a level of internal heterogeneity to the network evolution that
had never been noticed before, given the focus on global network sum-
mary statistics. This type of exploratory interaction between visualization
and analysis is one of the best reasons to push progress on dynamic
network visualizations.
Example 3: Ritual and Rebellion in the Classroom
Our final example presents a network representation of the streaming
interaction data in two classrooms observed by McFarland. Each inter-
action observed is represented by a directed arc. Statements that were
directed “to all” appear as a “star” of links. Direct interactions were
weighted as 1 (thick lines), and indirect interactions were weighted as
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Movie 5.—Online
1/n (where n p class s
).
ize Ties are coded as “social,” “task,” and “sanction”
to control the red, green, and blue color values of the ties. “Task” inter-
actions appear black, “social” interactions as blue, “praise” as green, and
“sanction” as red. The networks are shown in slices of 2.5 minutes du-
ration, so it is possible that multiple ties will exist between a given pair.
In all figures, the teacher is represented as a yellow node. Gender is coded
in the shape of the nodes (square p
,
male circle p
)
female and age in
color (tenth graders are light gray, eleventh graders are dark gray).
Class 173: Development of an Interaction Ritual
This example presents an orderly classroom, and movie 7 demonstrates
this order. To start, figure 8 presents the summary graph scores for class
173 comparable to those seen in the figures above. The bottom axis reveals
half-minute increments of class time so that a value of 70 indicates the
thirty-fifth minute of a class period. Viewing the figure, we see an im-
mediate difference with the previous friendship networks: transitivity
seems much less important in the conversation networks examined here.
On the other hand, reciprocity tends to be quite strong throughout the
observation period, though it admits to a high variance over time. Note
that none of the summary graph statistics converge toward a particular
value, suggesting that the interesting story in this setting deals with the
shape of change in the network rather than with the shape of the resultant
structure. Relational change remains relatively constant until 35 minutes
into the class period (see unit 70) when the level of interaction drops
significantly.
The movie for this class shows the transition across two primary activity
structures: recitation and group quizzes. Each type of segment calls upon
students to organize their behaviors in different sequential and relational
patterns. In the opening phase of the class, the teacher does some main-
tenance, collecting papers and making announcements as students slowly
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Movie 6.—Online
discard their sociable routines (minutes 0–2). Then the teacher settles the
class into a recitation routine concerning homework problems (minutes
3–28). Once the recitation routine is established, a clear ritual structure
emerges where the teacher broadcasts questions to the class, and indi-
vidual students sequentially reply to those questions as they move to the
center of the network image (Mehan 1979; Cazden 1988). At around min-
ute 26 (see unit 52) the teacher makes a joke (sociable broadcast) and
describes a humorous problem for the students to solve. Here, the task
retains the same structure of recitation but has a “blip” of bracketed social
activity. In the final phase of the class, there is a clear shift to dyads and
triads. Here the teacher asks students to get into assigned pairs and triads
to work quietly on their quiz. This final segment shows lower rates of
behavior that arise in an intermittent, localized nature. Near the end of
class, the teacher makes a final announcement, and then the students
break off and leave.
This movie illustrates how interaction dynamics can be represented in
a network form that captures both the sequential and relational nature
of ritual interaction. Moreover, it illustrates how the coordination and
mobilization of students through these routines is accomplished (i.e.,
through some sanctions and sociable activity, in this case). What we ob-
serve are two distinct kinds of relational “dances” and clear switches across
them.
Class 182: Ignoring authority
Moving from order to disorder, we now turn to class 182, with the now-
familiar summary scores presented in figure 9. As with the previous class-
room, we find no general pattern toward convergence in these values.
The amount of change and transitivity are generally higher in this class-
room. As will become clear, the higher transitivity levels follow from the
generally higher level of sociable activities.
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Fig. 7.—Nomination stabilization, Newcomb’s fraternity
Movie 8 shows the students in honors algebra 2 move through essen-
tially two phases of classroom activity. In the first phase, the teacher
lectures on and then invites discussion on student test performance
(minutes 0–15). The students ignore and deride this effort, so we see a
great deal of sociable interaction and conflict. About halfway through this
shortened class period (to make time for an assembly), the teacher shifts
into discussing and modeling homework problems with calculators. This
shift offers little change in form, as no one really listens and the sociable
routines continue. In the final 10 minutes of class, the teacher allows
students to work alone in their groups, and here their sociable interactions
can persist unabated (minutes 16–35). Throughout the class period, stu-
dents stay involved in their social affairs, and the teacher is forced to
interrupt them, but still fails to secure their attention.
The point of this movie is to show what disorder and lack of control
look like in dynamic form. While the movie shows that different patterns
of relations arise with each shift in activity, it does not show as clear a
shift as observed in the more controlled class above. This makes sense
since the class never really pays attention to the teacher’s prescribed
scripts for behavior. What we see is a high degree of social cliquing among
students that never abates in spite of the teacher’s sanctions efforts. It is
in the later phases of unabated social activity that we see the most stability
in network form.
In comparison to the other movies of discrete time, the movies of class-
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Fig. 8.—Reciprocity, transitivity, and change, class 173
room interaction and continuous time seem to be qualitatively different.
This may be more of an artifact of the examples and slices of time we
chose than of the methods. The simulation on balance and Newcomb’s
acquaintance story both show a progression in affective ties toward some
end state and uses of discrete notions of time. In classroom interactions,
the ties are represented in minutes of continuous class time, and since the
movie is specific to a single class period, there really is no story of pro-
gressive equilibrium in affective ties. Instead, the aim is to mobilize and
coordinate collective action in various formats (lecture, recitation, group
work, student presentations, etc.) and types of ties (task, social, etc.).
Hence, states of equilibrium are specific to tasks like lecture, recitation,
and group quizzes. While the shifts in rates of network change somewhat
align with changing ritual patterns, it is the movies that offer the most
meaningful evidence of change in relational sequence and form.
By using longer time slices (of say, class periods) and relating them over
the course of the school year, we may acquire something akin to the pattern
of tie formation in the Newcomb study or the balance simulation. A stable
pattern of behavior may eventually form in a classroom and act like a
central tendency (norm) adopted across tasks. The stability of this pattern
may even depend on how close ties reach an equilibrium state of balance
and transitivity. Future work will explore this empirical question further.
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Movie 7.—Online
SUMMARY AND CONCLUSION
This article has presented a first step toward developing a new class of
dynamic network visualizations. As with most methodological develop-
ments in social networks, the use and development of dynamic network
movies is grounded in the substantive need present in empirical research.
To build intuition about network dynamics effectively, a fine-grained tool
for visualizing relational change is necessary. We have focused on two
types of dynamic network visualizations: network flip books and dynamic
movies. The flip books are a combination of fixed node layout and dy-
namic social relations, where nodes remain in a constant position and
arcs fill in the holes among these nodes. They are particularly effective
at showing how sparse relational structures emerge from temporally dis-
aggregated social interaction. In contrast, fully dynamic network movies
allow nodes to move as a function of relational change. We have examined
three substantive examples, and in each case the movie makes it possible
to observe directly a relational feature that would be lost if we focused
only on summary statistics of the complete network.
The theoretical promise of network visualization rests in helping sci-
entists see their data. We hope that this type of visualization will spark
theoretical development as people are able to engage their data in new
ways. Abbott (2000) makes a similar point, when he argues, “Important
general theory always grows out of extensive empirical work; every great
sociological theorist has been a datahead” (p. 299). Social network movies
allow a limited form of data abstraction and exploration. We are neither
embedded directly in the relations themselves (which we could never do
due to the constraints of time and place) nor forced to limit our obser-
vations to one-dimensional summary statistics that filter out much of the
interesting temporal and relational variation in the data. Instead, like
much recent work in geography and meteorology, dynamic maps provide
a combined synthesis of information, allowing one to view the relevant
abstract features of a given interaction system.
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Dynamic Network Visualization
Fig. 9.—Reciprocity, transitivity, and change, class 182
Technically, we have described the use and performance of a number
of particular layout algorithms for building movies. More detail on con-
structing such movies can be found in the software description given in
appendix A (Bender-deMoll and McFarland 2002). In many ways these
algorithms are somewhat crude, so additional and ongoing research is
necessary. While we think it is much too early in the development of this
form of data visualization to make strong claims for a superior method,
a few summary statements of our experience are in order. In general,
layout methods should seek to minimize movement such that any change
can be directly related to a particular relational event. As with static
graph visualization procedures, simplicity is the goal. While judicious use
of colors, shapes, and sizes can help, too much of any of these elements
leads to a confusing visual cacophony.
With respect to particular graph layout algorithms, we have invested
the most time and had the most general success with the KK layout
algorithm. It is best at preventing node stacking, making it possible to
disentangle relational patterns at any given moment in the movie. KK
suffers, however, from superfluous local movement generated by changes
in the behaviors of others. Because KK pushes away from all nodes si-
multaneously, and due to details of its optimization procedure, nodes tend
to “float” around a space, filling in vacancies left by nodes that are drawn
into new spaces. This is evident in the Newcomb fraternity movie and
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Movie 8.—Online
can be seen as well in the movement of students around the teacher in
our classroom movies.
When asymmetric ties form a significant part of the relational story,
the peer-influence-based model seems to work well, though we find it very
sensitive to initial conditions and anchor points. When used with a con-
stant graph layout anchor, such as in the Newcomb example, movement
is often usefully limited to the most direct changes in graph structure.
When applied to our classrooms, for example, students tend not to cycle
around the initial circle, but remain fixed until they engage in a moving
interaction (see app. B, available in the online version of this article, for
examples).
The most obvious directions for extending network movies is to move
from an exploratory data analysis stage to a confirmatory analytic mod-
eling stage (McFarland and Bender-deMoll 2003). A good deal of headway
could be made, for example, by linking network movies to statistical
models of network change (Snijders 1998, 1990, 1996), or to models that
generate positional confidence intervals for nodes (Hoff et al. 2001). This
linkage would help us judge the degree of change in a network. This
linkage will be complicated, however, because much of the promise of
exploratory analysis is to identify elements from the data that are not
customarily included in global models. We suspect, however, that a closer
linkage between data and visualization will help us build better statistical
models.
APPENDIX A
Introduction to SoNIA Software
SoNIA (Social Network Image Animator) is a Java-based software pack-
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age for visualizing networks that change over time.15 SoNIA is being
developed as an open-source freeware project and is available with limited
documentation (see http://sonia.stanford.edu/). Work on SoNIA began ini-
tially out of a desire for a set of visualization tools specifically tailored
for dealing with network data that include explicit time information and
push the limits of the more traditional single-matrix approach to network
data collection. Although time is dealt with to some degree in existing
network packages such Pajek, it seemed useful to focus attention on al-
gorithms and techniques aimed at creating dynamic visualizations or an-
imated “movies” of network change. Also, implementations of the most
common layout algorithms rest on assumptions seldom discussed in the
network literature. SoNIA attempts to make some of these decisions more
explicit, provides some limited criteria for assessing the accuracy of a
given layout, and aims to produce layouts with a high degree of com-
parability and replicability. In addition, SoNIA serves a useful function
as a “browser” for time-based network data, and its modular construction
allows it to serve as test bed for the development and comparison of
network visualization algorithms.
SoNIA has the ability to read in a somewhat limited version of Pajek’s
arc-list-based “time network” format, and its own arc-list/spreadsheet style
format (.son files) in which tab-delimited columns control node and arc
attributes. Once data are loaded into SoNIA, the user has the ability to
choose a region of time to examine the duration and offset of the “slices”
used to bin the data and the layout algorithm to be employed. Currently
implemented are versions of Kamada Kawai, Furchterman-Riengold,
Moody’s Peer Influence, metric MDS, file coordinates, and circle. Plans
are to include GEM, Davidson-Harel, nonmetric MDS, and several other
multidimensional projection techniques. For each layout, SoNIA uses the
user’s bin criteria to divide up arc events in regions of time and aggregate
them to form network matrices to be fed into the layout algorithm. For
most algorithms, these matrices are converted to dissimilarities and sym-
metrized for use in distance computation. Several options are provided
for layout preprocessing (node starting positions, desired scaling, treat-
ment of isolates), postprocessing (rescaling, centering, etc.), as well as
parameters specific to each algorithm. For algorithms that use an opti-
mization technique, options are provided to control the “cooling schedule”
and stopping times, and feedback is provided about algorithm conver-
gence. Several algorithms (KK and FR) attempt to create layouts in which
15 SoNIA is currently under development by Dan McFarland and Skye Bender-deMoll.
The software, source files, installation instructions, and additional documentation are
available at http://sonia.stanford.edu/. Comments, suggestions, and programming as-
sistance would be greatly appreciated; please contact skyebend@stanford.edu.
1237
American Journal of Sociology
screen distances are proportional to values in the network matrix. For
most real-world networks, it is impossible to create a zero-distortion rep-
resentation. However, the degree of distortion can be estimated using a
modified version of Kruskal’s stress statistic to compare the matrix and
screen distances. This value and a “Shepard’s plot” showing the distri-
bution of distortions can be displayed.
The animation procedure for transitioning between layouts is similar
to “tweening,” in which a user-specified number of frames are displayed
showing gradual interpolation of nodes’ positions between successive lay-
outs. The transition takes place in “network time,” meaning that for real-
valued continuous data, node and arc additions and deletions between
the networks are shown in sequence as they occur. In addition, the time
coordinates for a “render slice” can be entered manually, allowing the user
to “browse” the data by displaying any arbitrarily sized region of time.
Node and arc attributes such as color, size, shape, labeling, and position
can be controlled from the input file (or to a limited degree in the program)
and are permitted to vary over time. SoNIA takes advantage of some of
Java’s 2D capabilities, which means graphics can be anti-aliased, and
arcs can have some degree of transparency (useful in situations were
multiplex ties exist). SoNIA has the ability to save out QuickTime movie
files of the network animation, a log file describing the sequence of op-
erations and parameter settings used to create the layout, and a series of
“slice” matrices for analysis in other SNA programs.
Because SoNIA is coded in Java, it is cross-platform compatible, and
there are many possibilities for extending its capabilities and integrating
it with other packages. SoNIA’s internal structure and Java’s modular
object-oriented design make it relatively easy to add additional layout
techniques and explore modifications. In addition, source files are avail-
able for inspection if the details of algorithm behavior are not clear from
documentation. However, a great deal of additional work is needed, par-
ticularly in the area of extending the design to facilitate communication
with other open-source projects and network software.
REFERENCES
Abbott, Andrew. 1997. “Of Time and Space: The Contemporary Relevance of the
Chicago School.” Social Forces 75:1149–82.
———. 2000. “Reflections on the Future of Sociology.” Contemporary Sociology 29:
296–300.
Abel, Tom, Greg L. Bryan, and Michael L. Norman. 2000. “The Formation and
Fragmentation of Primordial Molecular Clouds.” Astrophysical Journal 540:39–44.
Batagelj, Vladimir, and Andrej Mrvar. 2001. PAJEK, ver. 91. http://vlado.fmf.uni-lj.si/
pub/networks/pajek/
Bearman, Peter S., and K. Everett. 1993. “The Structure of Social Protest.” Social
Networks 15:171–200.
1238
Dynamic Network Visualization
Bearman, Peter S., Robert Faris, and James Moody. 1999. “Blocking the Future: New
Solutions for Old Problems in Historical Social Science.” Social Science History 23:
501–33.
Bearman, Peter S., James Moody, and Katherine Stovel. 2004. “Chains of Affection.”
American Journal of Sociology 110:44–91.
Bender-deMoll, Skye, and Daniel A. McFarland. 2002. SoNIA (Social Network Image
Animator). See http://sonia.stanford.edu/
Borgatti, S., M. G. Everett, and L. C. Freeman. 1999. UCINET V for Windows:
Software for Social Network Analysis, ver. 5.2.0.1. Natick, Mass.: Analytic
Technologies.
Brandes, Ulrik, Jorg Raab, and Dorothea Wagner. 2001. “Exploratory Network
Visualization: Simultaneous Display of Actor Status and Connections.” Journal of
Social
Structure
2
(4).
http://www.cmu.edu/joss/content/articles/volume2/
BradesRaabWagner./html
Cazden, Courtney B. 1988. Classroom Discourse: The Language of Teaching and
Learning. Portsmouth, N.H.: Heineman.
Chase, Ivan D. 1980. “Social Process and Hierarchy Formation in Small Groups: A
Comparative Perspective.” American Sociological Review 45:905–24.
Coleman, James S. 1961. The Adolescent Society. New York: Free Press.
Collins, Randall. 1981. “On the Microfoundations of Macrosociology.” American
Journal of Sociology 68 (5): 984–1014.
Cyram. 2004. NetMiner II, ver. 2.5.0a. Seoul: Cyram.
Danto, Arthur C. 1985. Narration and Knowledge. New York: Columbia University
Press.
Davidson, R., and D. Harel. 1996. “Drawing Graphics Nicely Using Simulated
Annealing.” ACM Transactions on Graphics 15:301–31.
Davis, James A. 1963. “Structural Balance, Mechanical Solidarity, and Interpersonal
Relations.” American Journal of Sociology 68:444–62.
———. 1970. “Clustering and Hierarchy in Interpersonal Relations: Testing Two
Graph Theoretical Models on 742 Sociomatrices.” American Sociological Review 35:
843–51.
Davis, James A., and Samuel Leinhardt. 1972. “The Structure of Positive Relations in
Small Groups.” Pp. 218–51 in Sociological Theories in Progress, vol. 2. Edited by
Joseph Berger, Morris Zelditch, and Benedict Anderson. Boston: Houghton Mifflin.
Doreian, Patric, Roman Kapuscinski, David Krackhardt, and Janusz Szczypula. 1996.
“A Brief History of Balance through Time.” Journal of Mathematical Sociology 21
(1–2): 113–31.
Doreian, Patrick. 1980. “On the Evolution of Group and Network Structure.” Social
Networks 2:235–32.
———. 1986. “On the Evolution of Group and Network Structure II: Structures within
Structures.” Social Networks 8:22–64.
Emirbayer, Mustafa. 1997. “Manifesto for Relational Sociology.” American Journal of
Sociology 103:281–317.
Emirbayer, Mustafa, and Jeff Goodwin. 1994. “Network Analysis, Culture, and the
Problem of Agency.” American Journal of Sociology 99:1411–54.
Freeman, Linton C. 2000a. “Visualizing Social Groups.” In Proceedings of the Section
on Statistical Graphics. American Statistical Association, http://moreno.ss.uci.edu/
groups.pdf
———. 2000b. “Visualizing Social Networks.” Journal of Social Structure 1 (1). http:
//www.cmu.edu/joss/content/articles/volume1/Freeman.html
Freeman, Linton C., Cynthia M. Webster, and Deirdre M. Kirke. 1998. “Exploring
Social Structure Using Dynamic Three-Dimensional Color Images.” Social Networks
20:109–18.
1239
American Journal of Sociology
Friedkin, Noah E. 1998. A Structural Theory of Social Influence. Cambridge:
Cambridge University Press.
Fruchterman, Thomas J. J., and Edward Reingold. 1991. “Graph Drawing by Force-
Directed Placement.” Software—Practice and Experience 21:1129–64.
Goffman, Erving. 1967. Interaction Ritual: Essays on Face-to-Face Behavior. Garden
City, N.Y.: Anchor Books.
———. 1981. Forms of Talk. Philadelphia: University of Pennsylvania Press.
Gould, Roger. 1995. Insurgent Identities: Class, Community, and Protest in Paris from
1848 to the Commune. Chicago: University of Chicago Press.
———. 2002. “The Origins of Status Hierarchies: A Formal Theory and Empirical
Test.” American Journal of Sociology 107:1143–78.
Handcock, Mark, and Martina Morris. 1999. Relative Distribution Methods in the
Social Sciences. New York: Springer.
Hinde, R. A. 1976. “Interactions, Relationships and Social Structure.” Man 11 (1): 1–17.
Hoff, Peter D., Adrian E. Raftery, and Mark S. Handcock. 2001. “Latent Space
Approaches to Social Network Analysis.” Working Paper no. 17. University of
Washington, Center for Statistics and the Social Science.
Johnsen, Eugene C. 1985. “Network Macrostructure Models for the Davis-Leinhardt
Set of Empirical Sociomatrices.” Social Networks 7:203–24.
———. 1986. “Structure and Process: Agreement Models for Friendship Formation.”
Social Networks 8:257–306.
Kamada, Tomihisa, and Satoru Kawai. 1989. “An Algorithm for Drawing General
Undirected Graphs.” Information Processing Letters 31:7–15.
Kretzschmar, Mirjam, and Martina Morris. 1996. “Measures of Concurrency in
Networks and the Spread of Infectious Disease.” Mathematical Biosciences 133:
165–95.
Laumann, Edward O., Peter Marsden, and David Prensky. 1983. “The Boundary
Specification Problem in Network Analysis.” In Applied Network Analysis: A
Methodological Introduction, edited by Ron S. Burt and M. J. Minor. London: Sage
Publications.
Laumann, Edward O., and Yoosik Youm. 1999. “Race/Ethnic Group Differences in
the Prevalence of Sexually Transmitted Diseases in the United States: A Network
Explanation.” Sexually Transmitted Diseases 266:250–61.
Leenders, Roger Th. A. J. 1996. “Longitudinal Behavior of Network Structure and
Actor Attributes: Modeling Interdependence of Contagion and Selection.” Pp. 165–84
in Evolution of Social Networks, edited by P. Doreian and Frans N. Stokman. New
York: Gordon & Breach.
Leifer, Eric M. 1988. “Interaction Preludes to Role Setting: Exploratory Local Action.”
American Sociological Review 53:865–78.
McFarland,
Daniel.
2001.
“Student
Resistance:
How
Formal
and
Informal
Organization of Classrooms Facilitates Student Defiance.” American Journal of
Sociology 107 (3): 612–78.
———. 2003. “Why Work When You Can Play? Dynamics of Formal and Informal
Organization in Classrooms.” In The Social Organization of Schooling: A Tribute to
Charles E. Bidwell, edited by Barbara Schneider and Larry Hedges. Thousand Oaks,
Calif.: Sage Publications.
McFarland, Daniel, and Skye Bender-deMoll. 2003. “Classroom Structuration: How
Interaction Patterns Get Reproduced and Transformed.” Working Paper. Stanford
University.
McGrath, Cathleen, Jim Blythe, and David Krackgardt. 1997. “The Effect of Spatial
Arrangement on Judgments and Errors in Interpreting Graphs.” Social Networks
19:223–42.
Mehan, Hugh. 1979. Learning Lessons: Social Organization in the Classroom.
Cambridge, Mass.: Harvard University Press.
1240
Dynamic Network Visualization
Moody, James. 2001a. “Peer Influence Groups: Identifying Dense Clusters in Large
Networks.” Social Networks 23:261–83.
———.2001b. “Race, School Integration, and Friendship Segregation in America.”
American Journal of Sociology 107 (3): 679–716.
———. 2002. “The Importance of Relationship Timing for Diffusion.” Social Forces
81:25–56.
———. 2003. “The Structure of a Social Science Collaboration Network: Disciplinary
Cohesion from 1963 to 1999.” American Sociological Review 69:213
Morris, Martina. 1993. “Epidemiology and Social Networks: Modeling Structured
Diffusion.” Sociological Methods and Research 22:99–126.
Morris, Martina, and M. Kretzschmar. 1997. “Concurrent Partnerships and the Spread
of HIV.” AIDS 11:641–48.
Nadel, S. F. 1955. The Theory of Social Structure. London: Cohen & West.
Nakao, K., and A. K. Romney. 1993. “Longitudinal Approach to Subgroup Formation:
A Re-Analysis of Newcomb’s Fraternity Data.” Social Networks 15:109–31.
Newcomb, Theodore M. 1961. The Acquaintance Process. New York: Holt, Rinehart
& Winston.
Newman, M. E. J. 2000. “The Structure and Function of Complex Networks.” SIAM
Review 45:167–256.
Padgett, John F., and Christopher K. Ansell. 1993. “Robust Action and the Rise of the
Medici, 1400–1434.” American Journal of Sociology 98:1259–1319.
Powell, Walter W., Douglas R. White, and Kenneth W. Koput. 2005. “Network
Dynamics and Field Evolution: The Growth of Interorganizational Collaboration
in the Life Sciences.” American Journal of Sociology 110 (4). In this issue.
Ridgeway, Cecilia, and Cathryn Johnson. 1990. “What Is the Relationship between
Socioemotional Behavior and Status in Task Groups?” American Journal of
Sociology 95 (5) :1189–1212.
Roy, William G. 1983. “The Unfolding of the Interlocking Directorate Structure of the
United States.” American Sociological Review 48:248–57.
Snijders, Tom A. B. 1990. “Testing for Change in a Digraph at Two Time Points.”
Social Networks 12:163–74.
———. 1996. “Stochastic Actor-Oriented Models for Network Change.” Journal of
Mathematical Sociology 21 (1–2): 149–72.
———. 1998. “Models for Longitudinal Social Network Data.” Manuscript. University
of Groningen.
———. 2001. “The Statistical Evaluation of Social Network Dynamics.” Sociological
Methodology 361–95.
Sørensen, Aage B., and Maureen T. Hallinan. 1976. “A Stochastic Model for Change
in Group Structure.” Social Science Research 5:43–61.
Suitor, J. J., Barry Wellman, and David L. Morgan. 1997. “It’s About Time: How,
Why and When Networks Change.” Social Networks 19 (1): 1–7.
Watts, Duncan J., and Steven H. Strogatz. 1998. “Collective Dynamics of ‘Small-World’
Networks.” Nature 393:440–42.
Weesie, Jeroen, and Henk Flap. 1990. Social Networks through Time. Utrecht: ISOR.
White, Harrison C., Scott A. Boorman, and Ronald L. Breiger. 1976. “Social Structure
from Multiple Networks I.” American Journal of Sociology 81:730–80.
Whyte, William Foote. 1943. Street Corner Society: The Social Structure of an Italian
Slum. Chicago: University of Chicago Press.
Zeggelink, Evelien P. H., Frans N. Stokman, and Gerhard G. Van De Bunt. 1996.
“The Emergence of Groups in the Evolution of Friendship Networks.” Journal of
Mathematical Sociology 21:29–55.
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