Structural Equivalence Relationship
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A Structural Equivalence Relationship is a graph nodes similarity measure based on ...
- AKA: Structural Relatedness.
- …
- Counter-Example(s):
- See: Blockmodel, Binary Directed Graph.
References
1987
- (Wang & Wong, 1987) ⇒ Yuchung J. Wang, and George Y. Wong. (1987). “Stochastic Blockmodels for Directed Graphs.” In: Journal of the American Statistical Association, 82(397).
1981
- (Holland and Leinhardt, 1981) ⇒ P. W. Holland, and S. Leinhardt. (1981), "An Exponential Family of Probability Distributions for Directed Graphs" (with discussion), Journal of the American Statistical Association, 76, 33-65.
1979
- (Sailer, 1979) ⇒ Lee Douglas Sailer. (1979). “Structural equivalence: Meaning and definition, computation and application." Social Networks, 1(1).
- ABSTRACT: This paper presents a generalization of the concept of “structural equivalence”, the key concept in algebraic approaches to the study of social networks. Two points in a graph or set of relations will be called “structurally related” if they are connected in the same ways to structurally related points.
It is suggested that this new definition suitably weakens Lorrain and White's categorical approach, and is more appropriate than CONCOR. Structural relatedness is compared to these approaches via several simple examples.
- ABSTRACT: This paper presents a generalization of the concept of “structural equivalence”, the key concept in algebraic approaches to the study of social networks. Two points in a graph or set of relations will be called “structurally related” if they are connected in the same ways to structurally related points.
1971
- (Lorrain & Harrison, 1971) ⇒ Francois Lorrain, and Harrison C. White. “Structural equivalence of individuals in social networks.” In: The Journal of mathematical sociology 1, no. 1 (1971): 49-80.
- ABSTRACT: The aim of this paper is to understand the interrelations among relations within concrete social groups. Social structure is sought, not ideal types, although the latter are relevant to interrelations among relations. From a detailed social network, patterns of global relations can be extracted, within which classes of equivalently positioned individuals are delineated. The global patterns are derived algebraically through a ‘functorial’ mapping of the original pattern. Such a mapping (essentially a generalized homomorphism) allows systematically for concatenation of effects through the network. The notion of functorial mapping is of central importance in the ‘theory of categories,’ a branch of modern algebra with numerous applications to algebra, topology, logic. The paper contains analyses of two social networks, exemplifying this approach.