ConvGraph: Community Detection of Homogeneous Relationships in Weighted Graphs

Héctor Muñoz,Ignacio González,Alfonso Mateos,Antonio Jiménez-Martín,Eloy Vicente

doi:10.3390/math9040367

Abstract

This paper proposes a new method, ConvGraph, to detect communities in highly cohesive and isolated weighted graphs, where the sum of the weights is significantly higher inside than outside the communities. The method starts by transforming the original graph into a line graph to apply a convolution, a common technique in the computer vision field. Although this technique was originally conceived to detect the optimum edge in images, it is used here to detect the optimum edges in communities identified by their weights rather than by their topology. The method includes a final refinement step applied to communities with a high vertex density that could not be detected in the first phase. The proposed algorithm was tested on a series of highly cohesive and isolated synthetic graphs and on a real-world export graph, performing well in both cases.

Highlights

We find that the detection rate of the ConvGraph method drops as density increases
This paper proposes a novel method, the ConvGraph method, for detecting highly cohesive and isolated communities in weighted graphs, where the sum of the weights is significantly higher inside than outside the communities
The performance analysis carried out on both synthetic graphs and a real-world export graph shows that the ConvGraph method is quite robust to noise, since the detection rate does not drop much if the ratio of the number of vertices to be detected to the total number of vertices in the graph is small

Summary

Introduction

A great deal of progress has been made with respect to knowledge of graphs and their properties, where computers can be used to represent many real networks using these types of models These real networks are characterized by a high level of order and organization; many low-degree vertices coexist with high or very high-degree vertices, and edges are distributed globally and locally, with high concentrations within special groups of vertices and low concentrations between these groups. These communities are, in short, groups of vertices that share properties and play a similar role in the graph but are differentiated from the others Nowadays, they represent one of the most interesting research lines in social network analysis due to their application in many areas such as biology or sociology, through medicine, to information technologies

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