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Components of complex systems are often classified according to the way theyinteract with each other. In graph theory such groups are known as clusters orcommunities. Many different techniques have been recently proposed to detectthem, some of which involve inference methods using either Bayesian or MaximumLikelihood approaches. In this article, we study a statistical model designedfor detecting clusters based on connection similarity. The basic assumption ofthe model is that the graph was generated by a certain grouping of the nodesand an Expectation Maximization algorithm is employed to infer that grouping.We show that the method admits further development to yield a stabilityanalysis of the groupings that quantifies the extent to which each nodeinfluences its neighbors group membership. Our approach naturally allows forthe identification of the key elements responsible for the grouping and theirresilience to changes in the network. Given the generality of the assumptionsunderlying the statistical model, such nodes are likely to play special rolesin the original system. We illustrate this point by analyzing several empiricalnetworks for which further information about the properties of the nodes isavailable. The search and identification of stabilizing nodes constitutes thusa novel technique to characterize the relevance of nodes in complex networks.

Stability of Maximum likelihood based clustering methods: exploring the backbone of classifications (Who is keeping you in that community?)