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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 for network theory construction:
• Graph theory
• Cognitive and structural balance
• Communication & information diffusion
• Social & generalized exchange
• Power-dependence
• Structural embeddedness
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: analyze kinship systems (Boyd 1969)
BALANCE THEORIES
Fritz Heider’s (1958) cognitive balance theory of attitude
change based on cognitive dissonance principles. When
beliefs are unbalanced, psychological stresses create
pressures to change a person’s sentiments (liking,
disliking) or unity (proximity, membership) into a congruent
pattern. Balance exists when a set of beliefs is equally
positive or negative; dissimilarities produce imbalance.
Balanced relations are evident in 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
P–O-X
Heider examined triads of positive and negative links off Person,
Other, and Object . Balance means positive product of the 3 ties.
Balanced:
BLAIR
O
P
BUSH
O
P
X
IRAQ
WAR
O
P
X
X
Unbalanced:
SCHRÖDER
O
P
BUSH
O
P
X
IRAQ
WAR
O
P
X
X
To restore balance, P must either change its sentiments about
O or X, or alter its beliefs about the O-X link.
STRUCTURAL BALANCE
Cartwright and Harary (1956) applied graph principles to
formalize and extend Heider’s cognitive balance theory to
structural balance of the behavioral links among triads.
Davis, Holland & Leinhardt (1979) studied clustering in graphs:
Any balanced graph divides into two cohesive subgroups, with
only positive ties internally (e.g., a friendship clique) & only
negative ties between clusters (e.g., feuding factions).
Actors avoid intransitive triads,
prefer to form transitive triads:
In a balanced graph, all the intransitive triads vanish.
UCINET transitivity program conducts a “triad census” of
a directed graph, tabulating the 16 MAN triad classes
(see diagrams in Wasserman & Faust p. 566).
INFORMATION DIFFUSION
Network models of communication and information diffusion help explain
patterns of innovation adoption (farming technology, family planning),
contagion in epidemics like HIV & Ebola, recruitment to high-risk social
movement actions (MS Freedom Summer). Diffusion analysts seek
answers to key question: “Who influences whom?”
When did Illinois physicians first prescribe new tetracycline drug?
Timing varied by network ties to early adopters (Coleman et al. 1966)
Uncertainty about outcomes compels more the risk-averse persons to
consult high-risk early adoptors for information, advice & reassurance.
Personal threshold hypothesis: As N of adoptors in ego-centric network
rises (both direct & indirect ties), pressures increase on ego to conform.
Relational network diffusion focuses on direct ties among
individuals. Structural network diffusion focuses on ego’s
position in the social structure, e.g., centrality & structural
equivalence (Valente 1995).
STRENGTH of WEAK TIES
Granovetter’s (1973) classic article on finding a job argued that
weak-tie relations (casual, indirect) give better access to new
information and opportunities. Strong ties (direct, emotionally
intense) restrict information flows from outside sources.
► Intimates (kin, close friends) share knowledge, norms, beliefs
► Although strong ties offer beneficial social support (“haven in a
heartless world”), they also result in impacted information & coercive
conformity to the social circle’s expectations (folkish society)
► Weak relations (acquaintances, coworkers) serve as bridges to
other social groupings having information & resources unavailable
within one’s intimate social circle; provide opportunities of individual
autonomy via unique structural location [Simmelian cross-cutting]
► Persons with many weak gain speedy advantages in learning
about and cashing in on new opportunities
► Thus, weak ties actually provide a strong form of social capital for
career advancement, financial manipulation, conference invitations
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 (the 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.
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 after a disaster (e.g., 9/11)
► Mafia criminal networks: code of omerta (see The Godfather)
► Scholarly publication reviews & promotion/tenure evaluations
Kula Ring A 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) blockmodel of generalized exchanges of
wives across the Aborigine marriage classes of Groote
Eylandt, where normative rules couldn’t be implemented.
POWER-DEPENDENCE
Richard Emerson (1962) theorized about the impact
of macro-network structures on dyadic exchange
processes and outcomes. Interconnected complex
exchanges reinforce inequalities (imbalances) and
change actor dependence on others.
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. Other ties mediate the dyad:
“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 EXPERIMENTS
Power-dependence theory spawned a cottage industry of
experimental & simulation studies based on computerized
laboratories. Sociologists tested theoretical propositions about
variations in communication network forms that give some
structural positions greater control over resources and increased
power to extract higher rewards from exchange transactions.
(For overviews see Willer [1992, 1999] and Molm [1997].)
► Power-dependence principles explain power distributions better
than does graph theory centrality (Cook et al. 1983)
► “Weak power” in resource acquisitions is highly conditioned by
actors’ experiences, orientations, & negotiation strategies
(Markovsky et al. 1993)
► Negotiated vs. reciprocal exchanges (Molm et al. 1999)
SOCIAL EMBEDDEDNESS
Mark Granovetter (1985) argued that economic
behaviors are embedded in social relations and
network structures that have substantial exogenous
influences on markets, firms, and workers.
EX: Ethnicity, kinship, and friendship ties reduce the risks of
opportunism & need for safeguards by small businesses.
Mutual trust lowers transaction costs and increases profitability
above market levels.
Embeddedness contradicts economists’ rational actors whose utilitymaximizing cost/benefit calculi use only prices & budget constraints,
without constraints from their contexts.
Embeddedness concepts influenced developments in
the “new economic sociology” (Uzzi 1996) and
organization studies (Dacin et al. 1999)
References
Barnes, J.A. and Frank Harary. 1983. “Graph Theory in Network Analysis.” Social Networks 5:235-244.
Blau, Peter M. 1964. Exchange and Power in Social Life. New York: Wiley.
Boyd, John Paul. 1969. “The Algebra of Group Kinship.” Journal of Mathematical Psychology 6:139167.
Cartwright and Frank Harary. 1956. “Structural Balance: A Generalization of Heider’s Theory.”
Psychological Review 63: 277-292.
Coleman, James S., Elihu Katz, and Herbert Menzel. 1966. Medical Innovation: A Diffusion Study. New
York: Bobbs Merrill.
Cook, Karen S., Richard M. Emerson, Mary R. Gillmore, and Toshio Yamagishi. 1983. “The Distribution
of Power in Exchange Networks: Theory and Experimental Results.” American Journal of Sociology
89:275-305.
Davis, James A. 1979. “The Davis/Holland/Leinhardt Studies: An Overview.” Pp. 51-62 in Network
Research, edited by Paul W. Holland and Samuel Leinhardt. New York: Academic Press.
Emerson, Richard M. 1962. “Power-Dependence Relations.” American Journal of Sociology 27:31-41.
Granovetter, Mark. 1973. “The Strength of Weak Ties.” American Journal of Sociology 78:1360-1380.
Granovetter, Mark. 1985. “Economic Action and Social Structure: The Problem of Embeddedness.”
American Journal of Sociology 91:481-510.
References
Harary, Frank and R.Z. Norman. 1953. Graph Theory as a Mathematical Model in Social Science.
Ann Arbor, MI: Universityof Michogan Institute of Social Research.
Heider, Fritz. 1958. The Psychology of Interpersonal Relations. New York: Wiley.
Homans, George C. 1958. “Social Behavior as Exchange.” American Journal of Sociology 63:597606.
Malinowski, Bronislaw. 1922. Argonauts of the Western Pacific. New York: 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
58:197-209.
Molm, Linda. 1997. Coercive Power in Social Exchange. New York:Cambridge University Press.
Uzzi, Brian. 1996. “The Sources and Consequences of Embeddedness for the Economic Performance
of Organizations: The Network Effect.” American Sociological Review 61:674-698.
Valente, Thomas W. 1995. Network Models of the Diffusion of Innovations. Cresskill, NJ: Hampton
Press.
Willer, David. 1992. “Predicting Power in Exchange Networks: A Brief History and Introduction to
the Issues.” Social Networks 14:187-211.
Willer, David. 1999. Network Exchange Theory. New York: Praeger.