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 of the SCAN algorithm.

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

“…The Improved HAMUHI (See III-A) presents a time complexity of O(T × alpha(G) × |E|), such that α(G) ≤ |E| is the arboricity of G [17], and T is the the number of iterations performed by the back-end DSS. Because T does not scale with the size of network (T ≈ 5) [18], it can be considered a constant factor in most practical cases, therefore we argue that this improved version keeps the same asymptotic time complexity of the original HAMUHI algorithm, that is, O(α(G) × |E|).…”

“…The Dynamic Structural Similarity (DSS) [18] determines the structural similarity of connected nodes in a graph by dynamically diffusing and capturing information beyond the immediate neighborhood of the analyzed nodes. This approach is based on the following intuition: Two nodes are structurally similar if they share an structurally similar neighborhood.…”

“…Cosine similarity) to perform community detection [17]. However, it has been shown that the local structural similarity presents some limitations that bypass important structural patterns of connections beyond the locality [18]. For that reason, we consider that a possibility to improve the quality of the community structure detected by the HAMUHI algorithm, is to support the cluster construction on a robust similarity measure capable of differentiating with higher quality inter-cluster edges from intra-cluster edges.…”

“…In this paper, we propose an improved version of the HAMUHI Algorithm. The improved version of HAMUHI is achieved after replacing the local structural similarity used in it, with the recently proposed Dynamic Structural Similarity [18]. Moreover, HAMUHI is further extended to leverage the disjoint community structure generated by itself to efficiently detect fuzzy and crisp overlapping community structure, while maintaining the same computational complexity.…”

A general approach for of schema matching problem: case of databases

“…However, this definition is insufficient to measure the similarity between two vertices it can be improved by taking into account the degrees of the vertices by defining the local structural similarity [165]:…”