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The Generalized Topological Overlap Matrix for Detecting Modules in Gene Networks

Systems biologic studies of gene and protein interaction networks have found that these networks are comprised of ‘modules’ (groups of tightly interconnected nodes). Module identification is an essential step towards understanding the whole network architecture. Here we will focus on module identification methods that are based on using a node dissimilarity measure in conjunction with a clustering method. More specifically, we introduce a general class of node dissimilarity measures based on the notion of ‘topological’ overlap, which has been found to be biologically meaningful in several applications. The resulting generalized topological overlap measure (GTOM) generalizes the standard topological overlap measure (TOM) introduced by (2002). Specifically, the m-th order version of this family is constructed by (i) counting the number of m-step neighbors that a pair of nodes share and (ii) normalizing it to take a value between 0 and 1. The main use of the GTOM measures is the identification of network modules (sets of tightly connected nodes). But it can also be used to define novel measures of node connectivity. These GTOM based connectivity measures go beyond the usual nodal degree (number of connections) by taking into account higher-order connections. We discuss the properties of the GTOM measures and provide empirical evidence that they are useful in the context of gene co-expression network analysis. We show that the original TOM proposed by (2002) favors the discovery of smaller modules whereas the higher-order GTOM’s favor larger modules.