Dynamic Structural Similarity on Graphs

Abstract: One way of characterizing the topological and structural properties of vertices and edges in a graph is by using structural similarity measures. Measures like Cosine, Jaccard and Dice compute the similarities restricted to the immediate neighborhood of the vertices, bypassing important structural properties beyond the locality. Others measures, such as the generalized edge clustering coefficient, go beyond the locality but with high computational complexity, making them impractical in large-scale scenarios. In this paper we propose a novel similarity measure that determines the structural similarity by dynamically diffusing and capturing information beyond the locality. This new similarity is modeled as an iterated function that can be solved by fixed point iteration in super-linear time and memory complexity, so it is able to analyze large-scale graphs. In order to show the advantages of the proposed similarity in the community detection task, we replace the local structural similarity used in the SCAN algorithm with the proposed similarity measure, improving the quality of the detected community structure and also reducing the sensitivity to the parameter $\epsilon$ of the SCAN algorithm.