On Connecting Network Analysis and Cluster Analysis

Actor equivalence is a fundamental concept for the analysis of network representations of social structure. In this paper it is shown that the partitioning of a network in terms of some kind of equivalence (e.g., structural or regular equivalence) is essentially a clustering problem. When searching for the best partition with standard clustering algorithms, a criterion function has to be defined, compatible with the chosen kind of equivalence. Such a criterion function can be constructed indirectly as a function of a compatible (dis)similarity measure between pairs of actors or directly as a function measuring the concordance of a given partition with an ideal partition for the chosen equivalence.