Fox

Abstract

Community detection is a hot topic for researchers in the fields of graph theory, social networks, and biological networks. Generally speaking, a community refers to a group of densely linked nodes in the network. Nodes usually have more than one community label, indicating their multiple roles or functions in the network. Unfortunately, existing solutions aiming at overlapping community detection are not capable of scaling to large-scale networks with millions of nodes and edges. In this article, we propose a fast-overlapping-community-detection algorithm—FOX. In the experiment on a network with 3.9 millions nodes and 20 millions edges, the detection finishes in 41 min and provides the most qualified results. The second-fastest algorithm, however, takes almost five times longer to run. As for another network with 22 millions nodes and 127 millions edges, our algorithm is the only one that can provide an overlapping community detection result and it only takes 533 min. Our algorithm is a typical heuristic algorithm, measuring the closeness of a node to a community by counting the number of triangles formed by the node and two other nodes in the community. We also extend the exploitation of triangle to open-triangle, which enlarges the scale of the detected communities.

LazyFox: fast and parallelized overlapping community detection in large graphs

“…We introduce L azy F ox , with its required input data and preprocessing, the employed metric , and the performed steps in the algorithm. We describe the parallelization that sets L azy F ox apart from F ox ( Lyu et al, 2020 ) and allows L azy F ox to scale across multiple CPU cores, and finally the performance measures employed here.…”

“…The WCC score has been adapted by Lyu et al (2020) in their F ox algorithm to enable faster overlapping community detection. This is the approach that L azy F ox is based on and we describe it in more detail in the ‘Methods’ section.…”

“…Thus, parallelized ( Prat-Pérez, Dominguez-Sal & Larriba-Pey, 2014 ) and distributed ( Saltz, Prat-Pérez & Dominguez-Sal, 2015 ) WCC versions have been proposed that allow multiple nodes at the same time to decide for changes to the community partition, so those decisions can be computed on separate threads or machines. Furthermore, computationally less expensive estimations of the WCC score have been suggested ( Prat-Pérez, Dominguez-Sal & Larriba-Pey, 2014 ; Lyu et al, 2020 ) to further improve runtime. Thereby, Lyu et al (2020) have found that a WCC -derived metric, , that particularly employs approximations of triangle counts in an algorithm they call F ox yields results very similar to calculating the exact count.…”

“…Furthermore, computationally less expensive estimations of the WCC score have been suggested ( Prat-Pérez, Dominguez-Sal & Larriba-Pey, 2014 ; Lyu et al, 2020 ) to further improve runtime. Thereby, Lyu et al (2020) have found that a WCC -derived metric, , that particularly employs approximations of triangle counts in an algorithm they call F ox yields results very similar to calculating the exact count. While their proposed metric allows F ox to compute overlapping communities on large networks with millions of edges, the implementation of F ox was not published making it hard to reproduce the results or to use them for further applications.…”

“…We here propose our tool for overlapping community detection, L azy F ox , that contains an implementation of the F ox algorithm. In addition, we extend the work of Lyu et al (2020) and combine it with ideas from Prat-Pérez, Dominguez-Sal & Larriba-Pey (2014) by introducing parallelism to leverage the advantage of modern multiprocessor systems to even further accelerate the algorithm.…”