Compare methods

	Triad Census	Structural Balance Theory
Field	Sociology	Sociology
Family	Process / pipeline	Process / pipeline
Year of origin	1970	1946 (Heider); 1956 (Cartwright & Harary)
Originator	Paul Holland & Samuel Leinhardt	Fritz Heider; formalized by Dorwin Cartwright & Frank Harary
Type	Enumeration of the 16 isomorphism classes of directed triads	Theory and graph-theoretic test for tension in signed relationships
Seminal source	Holland, P. W., & Leinhardt, S. (1970). A method for detecting structure in sociometric data. American Journal of Sociology, 76(3), 492–513.	Cartwright, D., & Harary, F. (1956). Structural balance: a generalization of Heider's theory. Psychological Review, 63(5), 277–293.
Aliases	triad count, triadic census, 16-type triad census, MAN triad census	balance theory, Heider balance, signed network balance, structural balance analysis
Related	4	5
Summary	The triad census counts how many of a directed network's three-actor subgroups fall into each of the 16 possible types of triad, providing a compact fingerprint of the network's local structure. Introduced by Paul Holland and Samuel Leinhardt in 1970, it is the standard way to test structural theories — balance, clustering, transitivity, ranked clusters — by comparing the observed distribution of triad types against what a random network would produce.	Structural balance theory analyzes networks whose ties carry a sign — positive for liking, alliance, or trust, negative for hostility or distrust — and asks which configurations are psychologically and socially stable. Originating in Fritz Heider's cognitive balance principle and given a graph-theoretic form by Dorwin Cartwright and Frank Harary in 1956, it predicts that signed networks evolve toward states free of the tension produced by inconsistent triads such as 'the friend of my enemy'.