SOCIAL NETWORK THEORIES:

Balance, Exchange & Embeddedness 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

Balance: cognitive & structural

Social exchange

Power-dependence

Network exchange theories

Social embeddedness

Graph Theory

Algebraic theory of semigroups (homomorphisms) also uses math formalization, e.g., kinship systems analysis (Boyd 1992)

► Like all mathematics, graph theory is a set of tightly interconnected tautologies

► Rigorous language used to state unproved axioms about two primitive terms (point, line) in discrete sets

► Logical deduction derives and proves new theorems

► But, validity of graph model’s implications for real social behaviors is often unclear

SNA has been tied to graph theory branch of finite mathematics (aka discrete math) since Harary & Norman (1953). Computer science is also grounded in this math. Many Social Networks articles use graph ideas, but “its theorems ... are generally neglected” (Barnes & Harary 1983).

Cognitive Balance Theories

Fritz Heider’s cognitive balance theory of attitudes towards people & social objects used cognitive dissonance principles.

If a person’s beliefs are unbalanced, psychological stresses will generate internal pressures to change either some of the sentiments (liking, disliking) or some 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 psychologically sustainable.

“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)

P – O - XHeider examined triads of positive and negative links of Person, Other, Object (X). Balance means a positive product of three lines: (-)(-)(+) = (+).

P

O

X

P

O

X

P

O

X

P

O

X

P

O

X

P

O

X

Balanced:

Unbalanced:

To restore balance in the triad, P must either change attitudes toward O or X, or alter belief about the O-X link. How might Bush restore balance to his Jacque Chirac-Iraq War triad?

BUSH

BLAIR

IRAQ WAR

BUSH

CHIRAC

IRAQ WAR

Balance Principles

► 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 _______________.

Cognitive balance ideas are captured by well-known folk sayings:

For directed relations the preference for balance typically leads to transformations resulting in transitive triads and avoiding intransitivity:

If A likes B and B likes C, then A should also like C. Seems true for friendships, but doesn’t work very well in love affairs & marriages!

If X dislikes Y and Y likes Z, then X should dislike Z. What are some examples in your own life?

CA

B

X

Y

Z

Structural BalanceCartwright and Harary (1956) applied graph principles to formalize & extend Heider’s cognitive balance theory to structural balance of behavioral ties among ordered triples.

UCINET’s transitivity program can conduct a “triad census” of any directed graph, counting the frequencies of 16 mutual, asymmetric, null (MAN) triad types with four dyad-character labels (see the next slide from James Moody; also in Wasserman & Faust 1994:566).

Davis, Holland & Leinhardt studied clustering in large graphs. They argued that tendencies towards balance should eliminate all the intransitive triads in a graph.

Any completely balanced graph will consist of either: (1) one huge clique (plus-set); or (2) be partitioned into two cohesive subgroups, each with only positive ties internally (e.g., a friendship clique) & only negative ties between those two cliques (e.g., feuding factions).

003

(0)

The 16 Triad Isomorphism Classes

012

(1)

102

(2)

021D

021U

021C

(3) (4) (5) (6)

Intransitive

Transitive

Mixed

111D 201 210 300

111U 120D

030T 120U

030C 120C

_________________Number of choices made_________________

SOURCE: after James Moody’s slides

MAN notation:

000 = # of Mutual, Asymmetric, Null

U = Up

D = Down

T = Transitive

C = Cyclic

Triad Census Examples

Two Cliques (Heider Balance)Triads either 300 or 102

Linear HierarchyEvery triad is 030T

Ranked Clusters (Hierarchy of Cliques)Triads: 300, 102, 003, 120D, 120U, 030T, 021D, 021U

(all)(all)

(all) (all)

(all)

W&F Ch.14 on methods to test hypothesized triad census distributions

Social Exchange TheoriesEconomics model assumes rational, utility-maximizing individuals who aren’t affected by social contexts. Exchange of valued goods & services occurs 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.

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’s advice to a bureaucratic subordinate, who gives back praise

George Homans (1958): Behavioral psychology propositions can fully explain social exchanges. Larger societal structures arise because rational self-interested persons repeat rewarded actions.

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 impacts of macro-network structures on direct dyadic exchanges and their outcomes. Complexly interconnected exchanges reinforce various structural inequalities (imbalances) and affect actors’ dependence on others.

Power is a structural relationship, inverse to the cost that one actor is willing to pay to another for an exchange. If actor B accepts a higher cost than actor A for an exchange, then B has a greater dependence on A: PAB = DBA

In a network of many actors, structural arrangements shape the prices & power that actors obtain through exchanges.

“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.”

Network Exchange Theory ExperimentsPower-dependence theory spawned a cottage industry of experimental & simulation studies based on computerized laboratories. Sociologists tested NET propositions about variations in exchange network forms, in which structural positions control differing resources and opportunities to

increase power & rewards by deals with alternative exchange partners.

Core design elements in NET experiments include: Differential distribution of valued resources among set of actors Structurally restricted opportunities for dyads to exchange Exchange relations link all actors into single network structure Actors seek profits by negotiating exchange prices with alters

Positive vs Negative ConnectionsExchange dyads B-A & A-C form triadic net A-B-C if exchange in one dyadic relation is contingent on whether exchange occurs in other dyad:

Experimental results typically find support for NET predictions:

► Power-dependence principles explain actor power distributions better than does graph theory centrality (Cook et al. 1983)

► “Weak power” in resource acquisitions depends on actor experiences, orientations, negotiation strategies (Markovsky et al. 1993)

► Negotiated, reciprocal, & generalized forms of social exchanges differently affect trust and commitment, risk-taking behavior, and perceived fairness and legitimacy (Molm et al. 1999)

1. A positive connection if exchange in one relation is contingent on exchange in another relation: Professor instructs a TA, who can then instruct a Student

2. A negative connection if one exchange is contingent on nonexchange in the other: Girl A can date Boyfriend B only if she does not date wanna-be Boyfriend C

Generalized ExchangesModern 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 Ring A complex system of visits & gift exchanges to foster social solidarity among the Trobriand Islanders, as described by Bronislaw Malinowski (1922). Bracelets and necklaces circulated through the islands in opposite directions. Persons who gave the most gifts generated the greatest dependencies in this obligatory network.

Bearman (1997) blockmodeled generalized exchanges of wives across the marriage classes of Groote Eylandt, where normative rules couldn’t be strictly implemented.

Contrary to neoclassical economics & Marxist economic determinism, Karl Polanyi (1944) proposed that economies are embedded within and influenced by macro-level social, political, cultural, institutional contexts.

“Our thesis is that the idea of a self-adjusting market implies a stark utopia. Such an institution could not exist for any length of time without annihilating the human and natural substance of society; it would have physically destroyed man and transformed his surroundings into a wilderness.”

Mark Granovetter (1985) revived Polanyi’s thesis, launching a “new economic sociology” emphasizing social construction of markets & embeddedness of economic actors in social networks and institutions.

Though sharing NET ideas, social embeddedness lacks formal rigor in application to large-scale socioeconomic systems, whose analysts must identify specific historical and spatial mechanisms of structural relations.

Social Embeddedness

Barnes, John. A. and Frank Harary. 1983. “Graph Theory in Network Analysis.” Social Networks 5: 235-244.

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.

Boyd, John Paul. 1992. “Relational Homomorphisms.” Social Networks 14:163-186.

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.

Granovetter, Mark. 1985. “Economic Action and Social Structure: The Problem of Embeddedness.” American Journal of Sociology 91:481-510.

Harary, Frank and R. Z. Norman. 1953. Graph Theory as a Mathematical Model in the Social Sciences. Ann Arbor, MI: Institute for Social Research.

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.

Polanyi, Karl. 1944. The Great Transformation: The Political and Economic Origins of Our Time. Boston: Beacon Press.

References