Dynamic Structural Similarity on Graphs

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.Comment: 8 pages, 7 figures, 1 table, Submitted for peer-review to the conference ASONAM 201

High-Quality Disjoint and Overlapping Community Structure in Large-Scale Complex Networks

In this paper, we propose an improved version of an agglomerative hierarchical clustering algorithm that performs disjoint community detection in large-scale complex networks. The improved algorithm is achieved after replacing the local structural similarity used in the original algorithm, with the recently proposed Dynamic Structural Similarity. Additionally, the improved algorithm is extended to detect fuzzy and crisp overlapping community structure. The extended algorithm leverages the disjoint community structure generated by itself and the dynamic structural similarity measures, to compute a proposed membership probability function that defines the fuzzy communities. Moreover, an experimental evaluation is performed on reference benchmark graphs in order to compare the proposed algorithms with the state-of-the-art.Comment: 8 pages, 5 figures, 3 tables, sent to peer-review to the International Symposium on Foundations and Applications of Big Data Analytics FAB 201