SOCIAL NETWORK THEORIES • Social network analysis is periodically accused of being merely “methods in search of a theory.” Theoretical underpinnings of network models often unstated or vague. • No orthodoxy dominates SNA, but several theoretical perspectives provide useful micro-level core concepts and explanatory propositions underpinning macro-networks: • Graph theory • Cognitive and structural balance • Social exchange • Power-dependence • Small World dynamics
Graph Theory • SNA tied to graph theory branch of finite mathematics since Harary & Norman (1953). Many Social Networks articles use graph ideas, but “its theorems..are generally neglected” (Barnes & Harary 1983). • ► Like all mathematics, graph theory is a set of interconnected tautologies • ► Rigorous language to state unproved axioms about two primitive terms (point, line) • ► Logical deduction to derive and prove new theorems • ► But, validity of graph model implications for real social behaviors is often unclear Algebraic theory of semigroups (homomorphisms) also a math formalization; EX: analysis of kinship systems (Boyd 1969)
Cognitive Balance Theories Fritz Heider’s cognitive balance theory of attitudes towards people & social objects used cognitive dissonance principles. “An attitude towards an event can alter the attitude towards the person who caused the event, and, if the attitudes towards a person and an event are similar, the event is easily ascribed to the person. A balanced configuration exists if the attitudes towards the parts of the causal unit are similar.” (Heider 1946:107) If a person’s beliefs are unbalanced, psychological stresses will generate internal pressures to change some of the sentiments (liking, disliking) or relationships (proximity, membership) into a more congruent pattern. Cognitive balance exists whenever a set of beliefs is equally positive or negative. Dissimilarities among beliefs produce imbalances that aren’t sustainable.
P – O - X Heider examined triads of positive and negative links of Person, Other, and Object (X). Balance means a positive product of three lines: (-)(-)(+) = (+). Balanced: BLAIR O O O BUSH P P P X X X IRAQ WAR Unbalanced: CHIRAC O O O BUSH P P P X X X IRAQ WAR To restore balance in the triad, P must either change his attitudes toward O or X, or alter his beliefs about the O-X link. How did Bush restore balance to his Jacque Chirac-Iraq War triad?
Balance Principles Cognitive balance ideas are captured by well-known folk sayings: • ► The friend of my friend is my _________________. • ► The enemy of my friend is my ________________. • ► The friend of my enemy is my ________________. • ► The enemy of my enemy is my _______________. The preference for balance typically leads in directed relationsto transformations resulting in transitive triads and avoiding intransitivity: B Y A C X Z If A likes B and B likes C, then A should also like C (but not in marriages!) If X dislikes Y and Y likes Z, then X should dislike Z.
Structural Balance Cartwright and Harary (1956) applied graph principles to formalize & extend Heider’s cognitive balance theory to structural balance of behavioral ties among ordered triples. Davis, Holland & Leinhardt studied clustering in large graphs. Tendencies towards balance should eliminate all intransitive triads. Any completely balanced graph will be either: (1) one huge clique; or (2) partitioned into two cohesive subgroups, each with only positive ties internally (e.g., a friendship clique) & only negative ties between the two cliques (e.g., feuding factions). UCINET’s transitivity program conducts a “triad census” of any directed graph, tabulating the frequencies of 16 mutual, asymmetric, null (MAN) triad types with four dyad-character labels (see the next slide by James Moody; also Wasserman & Faust 1994:566).
The 16 Triad Isomorphism Classes _________________Number of choices made_________________ (0) (1) (2) (3) (4) (5) (6) 003 012 102 111D 201 210 300 021D 111U 120D Intransitive Transitive 021U 030T 120U Mixed 021C 030C 120C SOURCE: James Moody, OSU
Social Exchange Theories Economics model assumes rational, utility-maximizing individual unaffected by social contexts. Exchanges of valued goods & services occur only when both parties’ subjective expected utilities are positive.Pricing mechanism provides sufficient information to clear the market. Transaction cost analysis in org’l studies based on economic exchange. George Homans (1958) - Behavioral psychology propositions can fully explain social exchanges. Larger societal structures arise because rational self-interested persons repeat rewarded actions. Peter Blau (1964) - Ambiguity in economic prices of indirect social exchanges: actors extend generalized credit which is repayable later (reciprocity norm, an obligation to return favors). EX: Supervisor gives job advice and assistance to a bureaucratic subordinate Power/inequality in a dyadic relation arises from ego’s control over some resource valued by alter who cannot find alternatives.
Power-dependence in Direct Exchanges Richard Emerson (1962) theorized about the impact of macro-network structures on dyadic exchange processes and outcomes. Complex interconnected exchanges reinforce structural inequalities (imbalances) and affect actors’ dependence on others. “A’s power over B is (1) directly proportional to the importance B places on the goals mediated by A and (2) inversely proportional to the availability of these goals to B outside the A-B relation.” • Power is a structural relationship, inverse to the cost that one actor willingly pays to another for an exchange. If actor B accepts a higher cost than actor A, then B has a greater dependence on A: PAB = DBA • In a network of many actors, structural alternatives shape the prices & power than actors obtain through exchanges.
Network Exchange Experiments Power-dependence theory spawned a cottage industry of experimental & simulation studies based on computerized laboratories. Sociologists tested theoretical propositions about variations in exchange network forms that giving structural positions greater control over resources and increased power to extract higher rewards from exchange transactions. • Core design features of exchange experiments include: • differential distribution of valued resources among set of actors • structurally restricted opportunities for dyads to exchange • exchange relations link all actors into a single network structure • actors seek profits by negotiating exchange prices withalters
Positive vs Negative Connections Exchange relations B-A and A-C form network B-A-C when exchange in one dyadic relation is contingent on exchange in the other dyad: 1. A positive connection if exchange in one relation is contingent on exchange in another relation: Professor instructs TA, who instructs Student 2. A negative connection if one exchange is contingent on nonexchange in the other: Girl A can date Boyfriend B only by not dating Boyfriend C • Experimental results support network exchange theory predictions • ► Power-dependence principles explain actor power distributions better than does graph theory centrality (Cook et al. 1983) • ► “Weak power” in resource acquisitions is highly conditioned by actors’ experiences, orientations, and negotiation strategies (Markovsky et al. 1993) • ► Negotiated, reciprocal, and generalized forms of social exchanges differently affect trust and commitment, risk-taking behavior, and perceived fairness & legitimacy (Molm et al. 1999)
Generalized Exchanges • Modern socioeconomic systems constructed as lengthy chains of indirect transactions, where direct reciprocity to a “giver” is often impossible. EX: Mentoring.Free-riding and opportunism problems; importance of interpersonal trust in complex transaction networks. • ► Giving blood to strangers after a disaster (e.g., 9/11) • ► Mafia criminal networks’ code of omerta (The Godfather) • ► Scholarly publication reviews & promotion/tenure evaluations Kula RingA complex system of visits and gift exchanges to foster social solidarity among the Trobriand Islanders, as described by Bronislaw Malinowski (1922). Necklaces and armbands circulated in opposite directions among islands residents. Persons giving the most gifts generate greatest dependencies in an obligatory network. Bearman’s (1997)blockmodelof generalized exchanges of wives across the Aborigine marriage classes of Groote Eylandt, where normative rules couldn’t be implemented.
It’s Small World After All Stanley Milgram’s (1967) less-infamous experiment explored how many first-name intermediaries were needed to deliver letters from random people in Omaha & Boston to “Sharon,” a Boston stockbroker. The unexpected average was six steps (paths), hence this play/movie’s title: • “Everybody on this planet is separated by only six other people. Six degrees of separation. Between us and everybody else on this planet. The president of the United States. A gondolier in Venice.... It’s not just the big names. It’s anyone. A native in a rain forest. A Tierra del Fuegan. An Eskimo. I am bound to everyone on this planet by a trail of six people. It’s a profound thought.... How every person is a new door, opening to other worlds.” • John Guare. 1990. Six Degrees of Separation: A Play. New York: Vintage. In Six Degrees (2003), Duncan Watts popularized recent network research by mathematicians, physicists & biologists. Watts & Steven Strogatz (1998) proposed a universal class of small-world network models, where clustering (C: high local density) & average shortest path length (L: separation) are a function ofp: the fraction of randomly rewired links.
The “New” Science of Networks Their class of simple small world networks occupies a broad region of p values where clustering C(p) is high relative to its random limit C(1), yet the average path length among actors L(p) is as “small” as possible. Fig 1: Watts-Strogatz model with parameter p randomly rewired for 1,000 actors connected to 10 nearest neighbors: They predicted that many very large “real-world” networks exhibit small-world features. Analyses of the movie-actor affiliation network (a.k.a. Kevin Bacon Game), the western U.S. power transmission grid, and nematode neural networks satisfied small-world criteria. Do generalizations of small-world models explain empirical collective dynamics: the speed of infectious epidemics (Ebola, Internet viruses), fashion crazes (Dutch tulips), even Amazon.com’s book-purchases?
References Bearman, Peter. 1997. “Generalized Exchange.” American Journal of Sociology 102:1383-1415. Blau, Peter M. 1964. Exchange and Power in Social Life. New York: Wiley. Cartwright, Dorwin and Frank Harary. 1956. “Structural Balance: A Generalization of Heider’s Theory.” Psychological Review 63:277-293. Cook, Karen S., Richard M. Emerson, Marry R. Gilmore, and Toshio Yamagishi. 1983. “The Distribution of Power in Exchange Networks: Theory and Experimental Results.” American Journal of Sociology 87:275-305. Davis, James A. 1967. “Clustering and Structural Balance in Graphs.” Human Relations 20:181-187. Emerson, Richard M. 1962. “Power-Dependence Relations.” American Sociological Review 27:31-41. Heider, Fritz. 1946. “Attitudes and Cognitive Organization.” Journal of Psychology 21:107-112. Heider, Fritz. 1958. The Psychology of Interpersonal Relations. New York: Wiley. Holland, Paul W. and Samuel Leinhardt. 1978. “An Omnibus Test for Social Structure Using Triads.” Sociological Methods & Research 7:227-256. Homans, George C. 1958. “Social Behavior as Exchange.” American Journal of Sociology 63:597-606. Malinowski, Bronislaw. 1922. Argonauts of the Western Pacific. New York: E.P. Dutton. Markovsky, Barry, John Skvoretz, David Willer, Michael J. Lovaglia, and Jeffrey Erger. 1993. “The Seeds of Weak Power: An Extension of Network Exchange Theory.” American Sociological Review 58:220-236. Molm, Linda D., Gretchen Peterson, and Nobuyuki Takahashi. 1999. “Power in Negotiated and Reciprocal Exchange.” American Sociological Review 64:876-890. Watts, Duncan and Steven Strogatz. 1998. “Collective Dynamics of ‘Small-World’ Networks.” Nature June 4:440-442.