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PART II
Workshop Papers
Note: Part II contains the papers as submitted to the workshop.
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OPENING ADDRESS
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Emergent Themes in Social Network Analysis: Results, Challenges, Opportunities
Ronald L. Breiger
University of Arizona
On behalf of the Workshop participants, ~ thank Anne Mavor (Director, Committee on
Human Factors, National Research Council / National Academy of Sciences) and Rebecca
Goolsby (US Office of Naval Research) for organizing this Workshop.
After a brief introduction to network analysis, ~ will identify the results of this enterprise
to date, emphasizing major themes that have emerged ~ will then turn to scientific and research
challenges that ~ see on the immediate horizon. and to those ~ perceive just beyond that horizon.
Finally, ~ will point to opportunities.
Thinking about social networks is ubiquitous and of Tong standing. It may be said that
kinship was the first social science, in that venous peoples' own cultural constructions of their
networks of kinship relations have seemed always to mix observation with analysis and with
proclamation (White, 1992: 290; Freeman, 20031. The 17th-century philosopher, Spinoza,
derived scores of logically interrelated propositions about a system that has the characteristics of
a basic social network situation, a system consisting of multiple relations such as loving,
hatred, and envy—among multiple actors (notably an acting person, an other, and an object).'
Spinoza's system is in many respects remarkably similar to the 20th-century theory of cognitive
balances that forms the backdrop to several papers presented at this Workshop. lLn Spinoza's
conception, actors change their initial opinions on the basis of network structure, as in some
contemporary forms of social influence modeling (see, e.g., CarIey's and FneUkin s papers
included in this volume), and multiple relations are key (which is the sense in which balance
theory provides one foundation for the paper of Macy et am.. A science of networks did not
emerge from Spinoza's speculative endeavor, or from the many others like it that are precursors
of contemporary network studies. Lacking was a commitment to the systematic observation and
modeling of actual behavior.
Military thinkers, too, have long found it natural to plan in terms of relations and forces.
CIausewitz (~832] 1976: 484) articulated a structuralist vision of warfare, writing that "in war.
more than anywhere else, it is the whole that governs all the parts, stamps them with its
character, and alters them radically." Keeping the dominant characteristics of both belligerents in
mind, "out of these characteristics a certain center of gravity develops, the hub of all power and
movement, on which everything else depends" (pp. 595-961. In countries subject to domestic
strife, CIausewitz continued. the center of gravity is generally the capital city. Among alliances.
it lies in "the community of interest," and in popular uprisings it is "the personalities of the
leaders and public opinion." It is "against these that our energy should be directed" (p. 5961. In
sham contrast to a concentrated network of forces, some more contemporary conflicts feature
protagonists who seek to "attain decisive strategic advantage by exploitation of the strength of
dispersed forces" (Boorman, 19G9: 1711. Two centuries after CIausewitz, social network
modeling is aiding in a reformulation of the "center of gravity" concept so that it is applicable to
extended command and control architectures (Dekker, 2001), and social network models of both
DYNAMIC SOCKS NETWO=MODELING AND ANALYSIS
19
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concentrated and dispersed forces inform thinking about information warfare (Pew and Mavor,
1998:301-19), netwars (Arauilla and Ronf~ltit ~n()11 anal the Hect~hili7~tinn of n~t`'lnrl ~ (~Orl-~T
et al., 2001).
~— — —1 ~~ ~ — ~ — ~ ~ ~ _^, ~ v—~~——^ ~ ~ ~~ ~4 ~^ A4~ ~ v ~ ~ ! 1~ \ ~ 01 1 ~ )
Freeman (2003) presents a monographic treatment of the history of social network
analysis; brief overviews are also available (Scott, 2000: 7-37; WelIman, ~1988] 1997: 21-291. At
the present time, the field is a recognized academic specialty pursued by a cross-disciplinary
network of sociologists, anthropologists, organization analysts, social psychologists, physicists,
statisticians, mathematicians, communication experts and people from many other fields.
Network analysts have a membership organization,3 professional journals,4 and a variety of
university centers of research. Network researchers are likely to agree with anthropologist Mary
Douglas (1973: 89) that "in a complex society, networks are the minimum level at which social
relations can be investigated." Four characteristics of the contemporary paradigm on network
analysis are identified by Freeman (20031: motivation by a structural intuition about specific
relationships linking social actors; grounding in systematic empirical data; heavy reliance on
graphic imagery; and use of mathematical and/or computational models
Results
Especially from the 1960s onward, major advances as well as cumulative building of
analytical methods and research findings have led to productive results in social network
modeling. Overviews and full treatments are available elsewhere.S ~ will briefly identify six
distinctive themes of network analysis that have emerged in recent decades.
I. Measures on nodes, arcs, and whole networks have been developed to exploit a variety
of relational insights. For example, the "centrality,' of an actor (call him Ego) as measured by
the number of ties he receives from other actors is a notion that is quite distinct from the same
actor's degree of "centrality" on the basis of the number of shortest paths through the network
that connect pairs of actors and that include Ego as an intermediary. (This is the distinction
between "degree" and "betweenness" variants of centrality; e.g., Freeman, 1979.) "Constraint"
is a measure of the extent to which Ego is tied to people who are invested in other of Ego's
contacts (Burt, 19921. The extent to which the acquaintance sets of two connected individuals
overlap has been captured by the faction of triplets in a network that are transitive (Holland and
Leinhardt? 1975), recently reintroduced as the "clustering coefficient" of Watts and Strogatz
( 19981. And entire networks may be characterized by their "density" of ties (the nronortion of
possible relationships among the actors that are observed to exist).
- ~—-- r--r~~~~~~- ~~
2. Analyses of role interlock have exploited the interpenetration of multiple networks
(such as "liking" and "disliking") on a given population of actors. Boorrnan and White (1976)
model role interlock by use of algebraic semigroups and homomorphisms; examples include the
study of "strength of weak ties" among advice-seeking on community affairs, business
partnerships, and social) relations of the community influentials in two small cities (Pattison,
1993: 2541. Recent studies of role interlock have made use of innovative statistical models for
network analysis, as in Lazega and Pattison's (2001) study of work relations, advice-seeking, and
friendship among partners and associates in three offices of a US law firm.
20
DYNAMIC SOCIAL NT:TWORKMODEL~G ED ^^YSIS
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3. Concepts of equivalence form the link between the individual-level data on ties and
connections, and the overall network macro-structure. Domain and White (1971: 80) sought to
locate "sets of individuals ... who are placed similarly with respect to all other sets of individuals,
to the extent that total relations and flows are captured by the aggregation of detailed relations
consonant with those equivalence sets of individuals." Structural equivalence captures sets of
actors each of whom has identical relations to all actors in a network of multiple types of tie.
Automo~phic equivalence identifies actors who have the same relation to similar types of others.
(A good metaphoric example of automorphic equivalence is the quarterbacks of opposing
football teams). More general forms of equivalence have also been developed (see, em, Batagelj
et al., 1992, Bor~atti and Everett, 1992; Pattison, 1993) and applied in studies such as Van
Rossem's (1996) analysis of international diplomatic, military, and economic exchanges.
Statistical estimation of models of network macro-structure has been an area of considerable
progress (Nowicki and SnijUers, 20011.
4. Duality refers to the idea (for example) that interpersonal networks based on common
membership in groups may be turned "inside out" to reveal networks among groups based the
number of members they share (Breiger, ~ 974, Pattison and Breiger, 20021. Thus, in addition to
defining networks on persons, networks may be defined on linkages between different levels of
structure. An example and extensions appear in Mische and Pattison's (2000) three-level study of
social movement activists, their organizational memberships, and venous projects in which they
engaged. Statistical modeling of affiliation data has been developed and applied to study
appearances of Soviet political elites at official and social events for ~ years during the Brezhnev
era (Faust et al., 20021. Innovative sampling schemes and analytical frames have been
developed for dual network situations (McPherson, 20011.
5. The study of social influence links networks of social relations to attitudes and
behaviors of the actors (Marsden and Fnedkin, 1994: 3; Robins et al., 20011. Analysts of social
influence model how an actor's attitudes or opinions are adjusted to those of the others who have
some influence on the actor (DeGroot, 19741. Frie&kin formal theory (1998) models the
equilibrium outcomes of influence processes and leads to testable predictions of opinion change.
From a different perspective, one viewing an organization's members as interdependent
entrepreneurs who cultivate status competition, Lazega (2001) studies collective action and the
evolution of mechanisms for self-governance among peers in a "collegial" (non-hierarchical)
organization. In their Workshop paper included in this volume, Michael Macy and his
collaborators demonstrate how the study of evolving group polarization can benefit from the
modeling of actors as computational agents.
G. Models and methods for visualizing networks have improved strikingly since Jacob
Moreno introduced the sociograrn in ~ 934. At that time the basic idea was to represent social
actors by circles and relationships by arrows connecting the circles. Increasingly in recent times
(see Freeman 2000), the battier between visualization and formal modeling has been
disappearing, as more powerful techniques for representation continue to be developed.
DYNAMIC SOCIAL N~TWO~MODEL~G ED ISIS
21
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22
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Figure 1. Florence network macro-structure. SOURCE: Figure 2.b on p. 1~77 in J.F. Padgett and C.K. Ansell. in Robust
Action and the Rise of the Medici. 1400-1434, American Journal of Sociology 98:12~9-1319, 1993. Reprinted by permission.
An illustration of how various of these themes might combine in a research application is
provided by Padgett and Ansell's (1993) study of the rise of the Medici family in fifteenth-
century Florence The data came (in some cases directly, in others via the work of histonans)
from the extensive archives in Florence, including tax assessments for the years 1403 and 1427
and a wealth of kinship, marriage, business, and census records. The data reflected in Figure
pertain to 92 families.
With respect to multiple networks: The graph in Figure ~ reports relations (coded
separately) of personal loans, patronage, friendship (coded by historians from extensive personal
letters that have been preserved), and the posting of surety bonds in another's behalf in order to
guarantee good behavior. By hypothesis, each network reports a potentially different quality of
relation, with the entire set of relations serving to comprise the structure.
With respect to types of equivalence: Pad=,ett and Ansell develop a method for
ag;,regating the 92 families into structurally equivalent sets relying heavily on their external ties
with outsiders, as well as on their internal relations. Figure ~ thus reports a macro-structure, a
reduced-form visualization of the network of relations among the identified aggregates of
families.
DYNAMIC SOCIAL NETWO~MODEL~G ED CYSTS
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With respect to network measures: The authors report that, among the Medicean families
at the top of Figure I, Freeman's measure of "betweenness" centrality (CB) is .362 for
intermarriages among the families; for the remaining families in the figure, it is a much lower
.198. The import is that the Medici family connected many other families that had few ties
among themselves; they served as a hub for this portion of the structure.
The authors' interpretation is roughly as follows. The traditional oligarchical families
portrayed in the lower portion of Figure ~ were highly interconnected. Dense ties, however, did
not lead to cohesive collective action in time of crisis, given the many status equals among the
oligarghs, each with a plausible claim to leadership. In shaIp contrast, the Medici family stood
as the gateway from its followers to the rest of the structure. This was an extraordinarily
centralized "star" or "spoke" system, with very few direct relations among the Medici partisans.
Thus, the rise of the Medici corresponded to a network strategy in which their follwers were kept
structurally isolated from one another (see also Padgett, 20011.
In my summary characterization of the results of social network analysis, ~ have recourse
to the subtitle of Wasserman and Faust's (1994) SOO-page compendium: "Methods and
Applications." ~ believe we now have a productive array of distinctive tools with which to build
impressive analyses along many lines of inquiry. Before we move to a qualitatively higher leve!
of progress in theoretical development, certain extant challenges will have to be met, and it is to
these that ~ now turn.
Challenges on the Horizon
Here ~ focus on scientific and research challenges on the immediate honzon, in the areas
of statistical modeling, data quality, and network sampling. A number of Workshop participants
are in the process of making breakthroughs in these areas.
Statistical Modeling
Statistical analysis of network ties is both important and difficult. It is important (among
other reasons) because it can allow us to distinguish pattern from random noise, and because it
enables us to assess comparatively a variety of hypotheses about the structures that underlie or
generate the network data that we observe. It is difficult because the units of observations (such
as the tie from person A to B and those from A to C and from B to A) are not independent.
Efforts dating from the 1930s to mode] the distribution of ties received by actors in social
networks (such as the binomial mode] of Paul Lazarsfeld's reported in Moreno and Jennings,
1938) recognized that "a change in position of one individual may affect the whole structure."6
A major line of investigation in the 1970s (e.g., Holland and Leinhardt, ~ 975) sought network
inferences from a more realistic embedding of non-independent relationships within triads of
social actors. In a major breakthrough, Holland and Leinhardt (1981) formulated an exponential
family of models (which they termed the pi family) that provided estimation of the probability of
an observed network conditioned on the number of ties sent and received by each actor (and the
network's overall density) and, simultaneously, on the two-person conf~;,urations (mutual,
DYNAMIC SOCIAL N~TWO^: MODELING ED ISIS
23
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asymmetric, and null-choice dyads) among the actors. Application of the mode! led to some
substantively important research, for example on decision-making in organizational fields
(Galaskiewicz and Wasserman, 19891.
Three problems with Wept model were to motivate further work. First, the advances of
Holland and Leinhardt's 1981 mode! entailed a return to the assumption of dyadic independence
(the assumption, e.g., that person A's choice of B is independent of A's choice of C), which is
surely unrealistic in many contexts. Second, because pi is essentially a null model, its ability to
characterize actual network data was poor. Third, degrees of freedom for assessing, the overall fit
of these model often depended on the number of actors in the network, thus violating the usual
assumptions about asymptotics in maximum likelihood estimation.
Recent work constituting fully a new breakthrough, however, has allowed the assumption
of dyadic independence to be rendered unnecessary in new families of more realistic models
based on hypotheses about the precise nature of network dependencies.7 These new models, as
formulated in particular by Wasserman, Pattison, and Robins (Wasserman and Pattison, 1996;
Pattison and Wasserman, 1999; Robins et al., 1999) go under the name of random graph models
or p* models. Formulating applications of these models to diverse network contexts, as well as
issues pertaining to estimation of the models, characterizes major challenges for current network
research. Because a number of papers presented at this Workshop pertain to these challenges,
will continue with a brief characterization of such models.8
It is useful for those without a strong statistics back;~,round to keep in mind that these
random graph (or p*) models encode hypotheses that "you can get your hands on," hypotheses
concerning definite features of observed social relations. Each such model asserts that a specific
collection of simple, concrete structures (tenned "configurations") compose the network as a
whose. Single networks as well as networks of multiple types of relation (such as co-worker and
socializing, in Lazega and Pattison's 2001 study of 71 partners and associates in a law firm with
offices in three cities) may be modeled with this approach.
There is also an equilibnum aspect to these random ;~,raph models, in that the presence or
absence of each possible tie in the network is estimated conditioning on the rest of the data. It
may be the case that, once these configurations are specified by an analyst, very standard
methods of estimation ("Iogit regression") are applicable. However, the resulting estimates do
not satisfy some of the usual assumptions (they are pseudo-likelihood estimates rather than full
maximum likelihood), and this point has occasioned a pond deal of n~l~litionn1 work Em. of
which is reported at this Workshop.
O ~ a ~ e ~~_.~~ ~~_ ~^
Several of the Workshop papers included in this volume may be located with respect to
the challenges of statistical modeling that ~ have reviewed. In his paper, Mark Handcock
investigates some of the consequences (for what he teens the degeneracy of the estimation
process) that result from the use of pseudo-likelihood estimation. He makes use of simulation
methods, known as Markov Chain Monte Cario (MCMC) methods, that allow estimation of
parameters such that the estimates are constrained to the non-degenerate part of the mode} space.
In his paper, Peter Hoff reviews an aDDroach (a form of generalized linear mixerl-~.ffe.rt~ morl~l~1
that he and his colleagues see as having particularly feasible means of exact parameter
~ , ~ ~ ~ ~ ^ v ~
24
DYNAMIC SOCKS NETWO=MODEL~G ED CYSTS
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estimation. A ~ ~ - - ~ ~ ~ -
An application of this approach to modeling political interactions of the pnmary
actors in Central Asian politics over the period 1989-1999 is presented in the DaDer of Michael
Ward and Peter Hoff in this volume.
.
Tom SnijUers has developed a model for the statistical evaluation of network dynamics
that has a certain relation to the random graph (p*) models (see SnijUers, 2001: 388-89~. In his
Workshop paper included in this volume SnijUers applies his mode! to the study of network
evolution and. in particular, to the evolution of a network's degree distribution (the number of
ties implicating each actor). Degree distribution has been the central focus of recent models of
social networks that have been formulated by physicists (see Watts and Strogatz~ ~ 998- and also
the papers in this volume by Eugene Stanley and by Christos Faloutsos). One of SnijUers'
principal findings that there is no general straightforward relation between the degree
distribution on one hand and structural aspects of evolution on the other~ontinues the debate
On the importance of degree distributions and, in particular, on whether such distributions
provide a major key to (or even a "universal law" governing) the evolution of social networks.
In Snijders' paper as well as the paper of Martina Morris, the question of what sorts of
parametenzations are appropriate for statistical models of social networks comes strongly to the
foreground. Stanley Wasserman and Douglas Steinley begin building a framework for analysis
how sensitive the results of network analysis are to the pecuTianties of the dataset as well as to
the parameters the analyst is attempting to estimate. Their paper in this volume reports, for
example. that interaction between different graph statistics (such as centralization and
transitivity) is crucial for robustness of estimation.
Elisa Jayne Bienenstock and Phillip Bonacich turn robustness from a technical issue to a
substantive one. In their Workshop paper they report a simulation study of different network
configurations (pinwheels, lattices, and so on). Their major measures are network efficiency and
vulnerability. They find for example that centralized communication networks are more efficient
but also more vulnerable to selective attacks on their most central members.
In another contribution that seeks to tun1 robustness from a technical issue to a
substantive one, Stephen Borgatti's Workshop paper develops two versions of what Borgatti
teens the key player problem: finding a set of nodes which, if removed' would maximally disrupt
communication among the remainin, nodes (KPP-|)? and finding a At of nnr1~.~ that in maims
connected to all other nodes (KPP -21.
~ A, ~ ~ .. TV I.,——All
The Workshop paper authored by Andrew Seary and William Richards reviews
eigenvector decomposition methods for network analysis. Their paper also moves in the
direction of investigating conditions for network stability and its disruption, as with their report
of a result from spectral decomposition that may be used to solve the longstanding problem of
dividing, a network into two sets with minimal connectivity between them.
Pattison and Robins (2002; see also Robins et al., 2001) have explored various sorts of
non-network information that can be incorporated into random-graph models—information such
as actor attributes, affiliations of persons with groups, and spatial layouts. Research on the
relation between geographic spatial arrangements and social networks is rapidly advancing
DYNAMIC SOCIAL NETWORK MODEM ID ISIS
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(Faust et al., 19991. In his paper for this Workshop, Carter Butts presents some fundamental
results on the relation of physical distance to network evolution. At least implicitly, this work
seems beneficial for the formulation of spatially oriented random graph models.
Data Quality and Network Sampling
Social networks have been measured in many ways, and the available research indicates
that these can make some claim to being reliable. though certainly imperfect, measures
(Marsden, 1990: 4561. A continuing challenge for network analysts is the formulation of
methods for the study of network data that are less than pristine with respect to reliability and
validity. Applications of network modeling to situations of increasing realism have heightened
concerns about missing data, data that seem unreliable, and actors (ranging from schoolchildren
to corporate executives) who may be behaving strategically in reporting or concealing their ties
to others. Related challenges concern the representativeness of network data. Network analysts,
including a number of Workshop participants, are currently engaged in confronting these
challenges.
Linton Freeman's paper for this Workshop reports a meta-analysis of twenty-one
methods applied to a single affiliation network. Assuming that there in ~ "trill" answer to th`=
- . ~ . .. , . ~
question or wnetner each Parr or persons belongs together in the same group, Freeman employs a
procedure—termed consensus analysis (Batchelder and Roruney, 1988) that allows
(simultaneously) the pooling of results from the twenty-one methods to uncover the most likely
candidates for "true" answers, and also quantitative assessment of the "competence" of each of
the twenty-one methods. Freeman's paper thus suggests that, in some situations (perhaps those
in which the venous methods applied are in the vicinity of the correct analysis of a structure),
intensive application of multiple analytical methods can compensate for data that are less than
perfect.
In her Workshop paper, Martina Moms is particularly interested in two rules governing
partner selection in sexual transmission networks: concurrency (number of partners) acne mixing
(the extent to which both partners share an attribute, such as race). These are examples of
network properties that can be measured with "local" network sampling strategies they dn not
. , . .. , . ~ . ~ .
--I----= ~ I---, —-—~ ~
require Data on ail relations ot all people In. a network. Going further, Months writes that "if
simple local rules [such as concurrency and mixing] govern partner selection, then these also
determine the aggregate structure in the network: What looks like an unfathomably complicated
system is, in fact, produced by a few key local organizing principles." In her paper included in
this volume, Morris combines this "local rules" approach with random graph models and
simulation strategies to understand the emergence of overall network structunng.
Robins, Pattison, and Woolcock (2002) provide random graph (p*) models for network
data containing non-respondents, without having to assume that the respondents missing are a
random sample. An earlier effort along a somewhat similar line is that of FneUkin (1998: 77-
78).
26
DYNAMIC SOCIAL NETWORK A1ODEL~G ED TRYSTS
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Cognitive social structure (Krackhardt, 1987; see also Cariey and Krackhardt, 1996) is an
~ _ _ ~ _ : _ _ 1 ~ _ _ _ 1 . ~ ~
a; approacn associated WIth a u~st~nct~ve tomcat of data collection. Each individual in a
network is asked to provide reports of whether each individual has a relationship with each other.
Thus, each individual reports a full matrix of data. This approach has implications for the
analysis of date qualify. Define there to be "consensus" (Krackhardt, 1987: 117) on the tie from
person i to person j if at least a stipulated fraction of all network members report that i indeed
sends that tie to j. This allows a calibration of self-reports against the reports of others.
T~ it: ~ ~~ J ~_1 . ~ ~ ~ ~ ~ ~ ~ ~ · , . · . . . . ~
~~ ~~ `v cop paper ~nc~ucea In tins volume, Alden Klovdahl reviews studies that
employ random walk sampling, designs, which involve random selection of a very small number
of individuals from a large population. Each person is interviewed in order to obtain (among
other things) a list of network associates. One of these is randomly selected to be the next person
interviewed. and so forth. Klovdahl discusses in his paper how he used just ~ 80 interviews (60
random walks of 2 steps each) to study network properties of a city of a quarter-million people.
All of the above efforts respond to the challenge of analyzing network data that is of less
than perfect quality. It will also be useful to encourage studies (such as the one of Costenbader
and Valente, 2002) of the comparative performance of network measures (such as venous
measures of actor centrality) in the presence of increasing amounts of missing data.
Challenges Just Over the Horizon
~ will now turn to scientific and research challenges that ~ envision as just beyond our
current honzon. These concern efforts to significantly extend, or to generalize or to move
beyond, the social networks paradigm as outlined in the first major section above. Here too, the
Workshop participants are among those leading the way.
I. There is increasing interest in moving beyond the analysis of social networks to
consider questions of how such analyses relate to design issues. Principles of network
governance may be extended to the consideration of how criminal or terrorist networks might
function most effectively (Milward and Raab, 20021. Asking what makes a network effective?
Arquilla and Ronfeldt (2001: 32443) point to five levels: organizational (where leadership
resides; how hierarchical dynamics may be mixed in with network dynamics), narrative (not
simply a "line.' with a "spin," but grounded expression of participants' experiences, interests, and
values), doctrinal (for example, preference for a leaderless form), technological (for example, use
of couriers or the internet to connect people), and social (for example, the use of kinship or
bonding experiences as bases for trust). In his Workshop paper included in this volume, David
Lazer is concerned with governance issues involved in information diffusion among policy
agencies. In their Workshop paper, Noshir Contractor and Peter Monge raise the question of
how theories of underlying network dynamics need to be modified to be applicable to the study
of adversarial networks. Of particular interest, Contractor and Monge formulate numerous
testable hypotheses drawn from a wide range of substantive theories, all pertaining to modeling
the emergence of networks within their multi-theoretical, multi-level (MTML) model.
2. Dynamic Network Analysis (DNA) is the name that Kathleen Carley gives to her
highly distinctive, highly innovative effort to push the envelope or network analysis. Not
DYNAMIC SOCKS N~TWO~MODEL~G AND TRYSTS
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directly related to models of network dynamics such as SnijUers' (reviewed in the previous
section), CarIey's approach has three hallmarks. First, it is meta-matnx, in a dramatic extension
of the "duality" concept discussed in the first section above. The meta-mat~x includes matrices
relating people to people (social networks), people to knowledge (knowledge networks), people
to events (attendance networks), events to each other (temporal orderings, and more. Second, the
ties in the meta-matnx are defined probabilistically, on the basis of cognitive inferencing or
cognitive change models or Bayesian updating techniques. Third, CarIey's approach employs
multi-agent network models; for example, learning mechanisms are specified and used to
dynamically adjust networks as the computational agents in them attend events, learn new
information' or are removed from the network. One principal focus of Cariey's approach is the
cognitive, and to a lesser extent the social, processes by which the networks in the meta-matrix
evolve.
As is Kathleen Cariey. Michael Macy is a leader in the area of self-organizing networks
and computational agents. In his Workshop paper coauthored with James Kitts and Andreas
Flache, Macy et al. model evolving polarization of group opinion space. They report some
surprising disjunctions between interactions among the actors c)n c)n~ love ~n(1 the. ~.m~r~inn
group structuring, on the other.
O ~ · ~~ In_ am_ _—~^ 4=,—~—id,
3. "At the beginning of the 2Ist century, a maverick group of scientists is discovering Mat
all networks have a deep underlying order and operate according to simple but powerful rules.
This knowledge promises to shed fight on the spread of fads and viruses, the robustness of
ecosystems, the vulnerability of economies~ven the future of democracy." Thus reads the dust
jacket of a recent popularized account (Barabasi, 2002) of work by several researchers trained in
physics who have developed distinctive lines of modeling for social (and other) networks.
Beginning with regular structures or the one hand and random structures on the other,
researchers within this new tradition (Watts and Strogatz, 1998) show that introducing small
changes into the "regular" structure leads to massive change this is the "small world" network
with a few "shortcuts" that bridge the structure. Researchers in this tradition emphasize power-
law distributions of choices made by actors (this is the "scale-free" property), according to which
a fiery few actors have a great many ties (in rough analogy to route maps of airlines that have
"hub" systems). These writers demonstrate that such networks have important implications for
diffusion of diseases and for many other properties such as those alluded to in the quotation at
this paragraph's beginning.
In their paper for this Workshop, E. Eugene Stanley and Shiomo HavIin review advances
in the modeling of scale-free networks and related work, and they propose a trajectory of future
research aimed at understanding how to optimize the stability of threatened netoworks. And the
Workshop paper of Chnstos Faloutsos and his co-authors reviews a wide range of results
concerning power laws applied to network data, in research that combines network analysis and
graph mining. ~ believe that these papers should be read in conjunction with that of SnijUers,
who argues (convincingly, in my view) for the desirability of a dynamic modeling, context that
explicitly incorporates features (such as transitivity, cyclicity, and subgrouping) in addition to the
degree distnbution that is emphasized in physicists' models.
28
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4. Moving beyond a structural approach to social network analysis by directly engaging
cultural issues is a challenge that is increasingly attracting attention.~° The emphasis of network
analysis on formal aspects of social structure often seems the opposite of a concern for culture
and cognition; indeed, in the early work on structural equivalence "the cultural and social-
psychological meanings of actual ties are largely bypassed .... We focus instead on interpreting
the patterns among types of tie" (White et al. 1976: 734). However, over the past decade a fusion
of concern across structural modeling and problems of culture, cognition, action, and agency has
been among the most important developments for an influential segment of the community of
networks researchers.
An important spur to network thinking about culture and cognition was White's
rethinking of network theory in his 1992 volume Identity and Control. White now wrote of
agency as "the dynamic face of networks," as motivating "ways of ... upendfin~] institutionfs]
arid a. initiatting] fresh action'? (pp. 315, 2451. White (1992) considered discursive "narratives"
and "stories,' to be fundamental to structural pursuits. writing that "stories describe the ties in
networks" and that "a social network is a network of meallings" (pp. 65, 671. Emirbayer and
Goodwin (1994), who charactenzed identity and Control in exactly this way (p. 1437), went on
to prod network analysts to conceptualize more clearly the role of "ideals, beliefs? and values,
and of the actors that strive to realize them" (p. 1446~. A more extensive review of this direction
for extending social network research is provided in Brei=,er (20031.
The Workshop paper of Jeffrey Johnson, Lawrence Palinkas, and James Boster moves in
a sense in the "opposite" direction: extending rigorous structural conceptions into the analysis
and interpretation of cross-cultural studies on the evolution of informal group roles in Antarctic
research stations. One funding for example is that groups that have a rich mix of informal role
properties fare better.
5. Actor-Network Theory (ANT) is an orientation within the ~'post-modern" branch of
contemporary science studies. The term "actor-network" is intended to mark the difficulties in
establishing clear boundaries between network actors and connections, between agency and
structure, and between network actors and those who analyze networks (Law and Hassard,
1999). Research within this tradition includes Latour's (~1984] 1988) rewriting of the history of
Louis Pasteur as the interpenetration of networks of strong microbes with networks of weak
hygienists, viewing the microbes as "a means of locomotion for moving through the networks
that they wish to set up and command" (p. 451. This line of work has had no influence at all on
social network analysts. There may however be some potential in developing formal, analytic
models that incorporate insights from this tradition concerning the hnd~7ncs of ties ,:?nH
connections, structure and agency, and reflexiviyv (relations between
actors).
~ ~~ A ^ ~,~~ ~ ~ ~ ^ ~ ~ ^ ~
, ~ .. analysts and network
Opportunities
I will conclude by summarizing my discussion of results and challenges, and by pointing
to opportunities.
DYNAMIC SOCIAL NETWORK MODELING AND ANALYSIS
29
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As to results, we row have a large number of spectacularly useful methods and
applications. We have numerous studies of real-worId processes. There is a remarkable degree
of consensus among, researchers on the fundamentals of the approach, and a notable cumulation
of results.
The challenges that ~ see concern the development of research syntheses at the theory-
data interface. We need improved network statistical models. We need to further the
development of models that are at once validated, robust, and concerned with network dynamics.
We need to continue to improve methods for dealing with network sampling. We need to
continue to explore ways to significantly extend, or to generalize, or to move beyond the static
social networks paradigm, by embedding network models and research within the wider array of
concerns that ~ have sketched in the preceding section.
This Workshop will play an important role in furthering the kind of communication and
interchange that is necessary, among many of the leading researchers in the field. In pointing, to
future opportunities, ~ will paraphrase David Lazer's paper, hoping that he won't mind that ~ take
one of his conclusions slightly out of context, ~ conclusion that he labels a countenntuitive
governance prescription. In my version, the conclusion is that as research groups receive more
information regarding what other research groups are doing, incentives for all such shrouds to
~~ a _= ~ ~ ^~ v_~. ~~ ~~l~l-~ lie in
joining resources with innovation in pursuing the scientific challenges that confront us.
continue innovating. and thus creating knowlerl~e Hi h`= inr~r~.nc~r] nils nnn~rt~lniti~c:
30
DYNAMIC SOCIAL NETWORK HODEL~G kD ISIS
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Endnotes
For example, Proposition 35 in Spinoza's Ethic ([1677] 1923) reads: "If I imagine that an
object beloved by me is united to another person by the same, or by a closer bond of friendship
than that by which ~ myself alone hold the object, ~ shall be affected with hatred towards the
beloved object itself, and shall envy that other person."
Fritz Heider, who formulated balance theory in the ~ 940s, writes that he came to the theory by
reading and reconsidering Spinoza's work (Heider, 19791.
3 The International Network for Social Network Analysis (INSNA), web address
http://www. sfu.ca/~insna/.
4 Social Networks (published by Elsevier), the Journal of Social Structure (an electronic journal,
available on-line at http://www2.heinz.cmu.edu/project/INSNA/joss/), and Connections
(published by INSNA).
5 See in particular the monographic reviews of Wasserman and Faust (l994), DeGenne and
Forse (~1994l 1999), and Scott (9000) as well as the succinct overviews of Wellman (~1988]
1997) and Braider (20031.
6 InforTnation in this and the following paragraphs is condensed from the review of statistical
modeling of networks in Breiger (2003~.
7 The analyst is allowed to specific dependencies among any ties in the network that share a
node.
s See also the introduction in Anderson et al. (1999) as well as the cited papers of Wasserman,
Pattison, and Robins.
9 ~ am grateful to Philippa Pattison for reminding me of this point.
it This paragraph and the next draw directly on Breiger (20031.
DYNAMIC SOCIAL NETWORK MODELING ED ISIS
31
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36
DYNAMIC SOCKS NETWO=MODEL~G ED ^^YSIS
Representative terms from entire chapter:
social network
