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
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).
► 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
Algebraic theory of semigroups (homomorphisms) also uses
math formalization, e.g., kinship systems analysis (Boyd 1992)
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 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.
P–O-X
Heider examined triads of positive and negative links of Person, Other,
Object (X). Balance means a positive product of three lines: (-)(-)(+) = (+).
Balanced:
BUSH
BLAIR
O
O
P
P
X IRAQ WAR
Unbalanced:
BUSH
P
CHIRAC
O
O
P
X
X
O
P
X IRAQ WAR
O
P
X
X
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?
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 _______________.
For directed relations the preference for balance typically leads to
transformations resulting in transitive triads and avoiding intransitivity:
B
A
Y
C
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!
X
Z
If X dislikes Y and Y likes
Z, then X should dislike Z.
What are some examples
in your own life?
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. 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).
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).
The 16 Triad Isomorphism Classes
_________________Number of choices made_________________
(0)
(1)
(2)
(3)
(4)
(5)
003
012
102
111D
201
210
021D
111U
120D
MAN notation:
000 = # of Mutual,
Asymmetric, Null
(6)
300
Intransitive
Transitive
U = Up
021U
030T
120U
021C
030C
120C
D = Down
Mixed
T = Transitive
C = Cyclic
SOURCE: after James Moody’s slides
Triad Census Examples
(all)
Linear Hierarchy
Every triad is 030T
(all)
(all)
Two Cliques (Heider Balance)
Triads either 300 or 102
(all)
(all)
Ranked Clusters (Hierarchy of Cliques)
Triads: 300, 102, 003, 120D, 120U, 030T, 021D, 021U
W&F Ch.14 on methods to test hypothesized triad census distributions
Social Exchange Theories
Economics 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.
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’s advice
to a bureaucratic subordinate, who gives back praise
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.
“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 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.
Network Exchange Theory Experiments
Power-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 Connections
Exchange 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:
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
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)
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 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.
Social Embeddedness
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.
References
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.