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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 envyamong 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 &411~ \ ~ :au`D~m ~0 ~A,}= ail If_ DRUM .. .... CO~DOb`= ~ .4 ,.) f If I/ ,7 -~! ~ .. C~' . . . / ALUM '50~0~ RCND{!=Ll ~ 1~ r . ~ I. A. Abuzz' ? .1 ~ f' \\ amam my i' ~4.E ~ .. _ _ _ it. ~ ~~c~  _ _ _ _ .` Aid \'\, .~] ~~ BIBOf ~LUlI . . . . . . . ~pCS'"~1eS: Be.- . }tried of ~ 88t ~ ~ d 4 $ ~ ~ . 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 modelsinformation 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 25

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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 proceduretermed 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 27

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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 DYNAMIC SOCIAL IJETWO=MODEL~G kD TRYSTS

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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