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Hierarchical Clique Structures

Edmund R. Peay
Sociometry
Vol. 37, No. 1 (Mar., 1974), pp. 54-65
DOI: 10.2307/2786466
Stable URL: http://www.jstor.org/stable/2786466
Page Count: 12
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Hierarchical Clique Structures
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Abstract

The clique, as defined in graph theory, provides a rigorous abstraction of the idea of a "tightly knit" subset of a set of elements. A number of methods, known as "clique detection procedures", exist for finding the cliques of a given graph, but they are generally rather complex and unwieldy. When the graph is generalized to the network by permitting quantitative relationships, a hierarchical clique structure (i.e., an ordered sequence of clique groupings) can be derived. An literative method for finding hierachical clique structures is presented, which can also be used as a more conceptually straightforward clique detection procedure for graphs. The problem of finding a hierarchical clique structure in a network is formally related to clustering for proximity data, and the method presented also constitutes a types of hierarchical clustering procedure.

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