SOCIAL NETWORK THEORIES: Balance, Exchange

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SOCIAL NETWORK THEORIESBalance, 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

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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 models
implications for real social behaviors is often
unclear
Algebraic theory of semigroups (homomorphisms)
also uses math formalization, e.g., kinship
systems analysis (Boyd 1992)
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Cognitive Balance Theories
Fritz Heiders 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 1946107)
If a persons 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 arent psychologically sustainable.
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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
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 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?
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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
Y
C
A
X
Z
If A likes B and B likes C, then A should also
like C. Seems true for friendships, but doesnt
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?
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Structural Balance
Cartwright and Harary (1956) applied graph
principles to formalize extend Heiders
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).
UCINETs 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 1994566).
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The 16 Triad Isomorphism Classes
_________________Number of choices
made_________________
(0)
(1)
(2)
(3)
(4)
(5)
(6)
003
012
102
111D
201
210
300
MAN notation 000 of Mutual, Asymmetric,
Null U Up D Down T Transitive C Cyclic
021D
111U
120D
Intransitive
Transitive
021U
030T
120U
Mixed
021C
030C
120C
SOURCE after James Moodys slides
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Triad Census Examples
(all)
(all)
Linear Hierarchy Every triad is 030T
(all)
(all)
(all)
Two Cliques (Heider Balance) Triads either 300 or
102
Ranked Clusters (Hierarchy of Cliques) Triads
300, 102, 003, 120D, 120U, 030T, 021D, 021U
WF Ch.14 on methods to test hypothesized triad
census distributions
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Social Exchange Theories
Economics model assumes rational,
utility-maximizing individuals who arent
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
orgl 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 Supervisors advice to a
bureaucratic subordinate, who gives back praise
Power/inequality in a dyadic relation arises from
egos control over some resource valued by alter
who cannot find alternatives.
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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.
As 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.
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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

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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)
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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 couldnt be strictly implemented.
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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 Polanyis 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.
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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
1021383-1415. Blau, Peter M. 1964. Exchange and
Power in Social Life. New York Wiley. Boyd, John
Paul. 1992. Relational Homomorphisms. Social
Networks 14163-186. Cartwright, Dorwin and
Frank Harary. 1956. Structural Balance A
Generalization of Heiders Theory. Psychological
Review 63277-293. 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 87275-305. Davis,
James A. 1967. Clustering and Structural Balance
in Graphs. Human Relations 20181-187. Emerson,
Richard M. 1962. Power-Dependence Relations.
American Sociological Review 2731-41. Granovetter
, Mark. 1985. Economic Action and Social
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Fritz. 1946. Attitudes and Cognitive
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