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Role-similarity based comparison of directed networks

The widespread relevance of complex networks is a valuable tool in the analysis of a broad range of systems. There is a demand for tools which enable the extraction of meaningful information and allow the comparison between different systems. We present a novel measure of similarity between nodes in different networks as a generalization of the concept of self-similarity. A similarity matrix is assembled as the distance between feature vectors that contain the in and out paths of all lengths for each node. Hence, nodes operating in a similar flow environment are considered similar regardless of network membership. We demonstrate that this method has the potential to be influential in tasks such as assigning identity or function to uncharacterized nodes. In addition an innovative application of graph partitioning to the raw results extends the concept to the comparison of networks in terms of their underlying role-structure.