Fast cluster-based computation of exact betweenness centrality in large graphs

Cecile Daniel,Eugenio Zimeo,Lorenzo Goglia,Angelo Furno

doi:10.1186/s40537-021-00483-1

Abstract

Nowadays a large amount of data is originated by complex systems, such as social networks, transportation systems, computer and service networks. These systems can be modeled by using graphs and studied by exploiting graph metrics, such as betweenness centrality (BC), a popular metric to analyze node centrality of graphs. In spite of its great potential, this metric requires long computation time, especially for large graphs. In this paper, we present a very fast algorithm to compute BC of undirected graphs by exploiting clustering. The algorithm leverages structural properties of graphs to find classes of equivalent nodes: by selecting one representative node for each class, we are able to compute BC by significantly reducing the number of single-source shortest path explorations adopted by Brandes’ algorithm. We formally prove the graph properties that we exploit to define the algorithm and present an implementation based on Scala for both sequential and parallel map-reduce executions. The experimental evaluation of both versions, conducted with synthetic and real graphs, reveals that our solution largely outperforms Brandes’ algorithm and significantly improves known heuristics.

Highlights

The massive amount of data available today in many domains is often originated by complex systems that can be modeled as graphs where network centrality is exploited for identifying important nodes of the modeled systems
We focus on unweighted graphs while its extension to weighted ones can be obtained by substituting the breadth-first search (BFS) with Dijkstra algorithm
Bridges and articulation vertices are edges and nodes, respectively, whose removal from a graph leads to a new graph with a greater number of connected components; degree-1 vertices are leaf nodes which, considered as source and targets, contribute to the computation of betweenness centrality (BC) of crossed nodes; identical vertices are the ones characterized by the same neighbors and, by the same BC values; side vertices are nodes such that the graphs induced by their neighbors are cliques and they are not crossed by shortest paths

Summary

Introduction

The massive amount of data available today in many domains is often originated by complex systems that can be modeled as graphs (e.g., social networks, transportation networks, computer networks, service networks, etc.) where network centrality is exploited for identifying important nodes (or edges) of the modeled systems. Bridges and articulation vertices are edges and nodes, respectively, whose removal from a graph leads to a new graph with a greater number of connected components; degree-1 vertices are leaf nodes which, considered as source and targets, contribute to the computation of BC of crossed nodes; identical vertices are the ones characterized by the same neighbors and, by the same BC values; side vertices are nodes such that the graphs induced by their neighbors are cliques and they are not crossed by shortest paths By using all these techniques, the authors achieve significant speedup with different kinds of graphs. Incremental and approximated computations are approaches for specific classes of applications that regard slowly changing graphs or rank-based exploitation of BC, respectively, which we consider out of the scope of this paper

Background

This is the part of contribution due to w as a destination

Findings

Conclusion