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:
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 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 relations 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
(but not in marriages!)
X
Z
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)
003
012
102
111D
201
210
021D
111U
120D
(6)
300
Intransitive
Transitive
SOURCE: James Moody, OSU
021U
030T
120U
021C
030C
120C
Mixed
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 with alters
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 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.
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 of p: 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 smallworld features. Analyses of the movieactor 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.