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Structural Equivalence×Triad Census×
FieldSociologySociology
FamilyProcess / pipelineProcess / pipeline
Year of origin19711970
OriginatorFrançois Lorrain & Harrison WhitePaul Holland & Samuel Leinhardt
TypeEquivalence relation grouping actors with identical tie patternsEnumeration of the 16 isomorphism classes of directed triads
Seminal sourceLorrain, F., & White, H. C. (1971). Structural equivalence of individuals in social networks. The Journal of Mathematical Sociology, 1(1), 49–80. DOI ↗Holland, P. W., & Leinhardt, S. (1970). A method for detecting structure in sociometric data. American Journal of Sociology, 76(3), 492–513. DOI ↗
Aliasesstructural equivalence analysis, positional equivalence, Euclidean equivalence of actors, equivalence classestriad count, triadic census, 16-type triad census, MAN triad census
Related54
SummaryStructural equivalence identifies actors who occupy the same position in a network because they have identical ties to identical others. Defined by François Lorrain and Harrison White in 1971, it formalizes the idea that two people are interchangeable in the social structure when they relate to exactly the same set of third parties, and it provides the foundation for partitioning networks into positions and building blockmodels.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.
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ScholarGateCompare methods: Structural Equivalence · Triad Census. Retrieved 2026-06-24 from https://scholargate.app/en/compare