Group Centrality Maximization for Large-scale Graphs

TL;DR

This paper introduces GED-Walk centrality, a new scalable group centrality measure based on walks of any length, with algorithms that efficiently approximate and maximize it, outperforming existing methods on large graphs.

Contribution

The paper proposes GED-Walk centrality, a novel submodular measure inspired by Katz centrality, along with efficient approximation algorithms for large-scale graphs.

Findings

GED-Walk improves performance on graph classification tasks.

Maximization of GED-Walk is significantly faster than existing measures.

Algorithms scale linearly and handle graphs with tens of millions of edges.

Abstract

The study of vertex centrality measures is a key aspect of network analysis. Naturally, such centrality measures have been generalized to groups of vertices; for popular measures it was shown that the problem of finding the most central group is $\mathcal{NP}$-hard. As a result, approximation algorithms to maximize group centralities were introduced recently. Despite a nearly-linear running time, approximation algorithms for group betweenness and (to a lesser extent) group closeness are rather slow on large networks due to high constant overheads. That is why we introduce GED-Walk centrality, a new submodular group centrality measure inspired by Katz centrality. In contrast to closeness and betweenness, it considers walks of any length rather than shortest paths, with shorter walks having a higher contribution. We define algorithms that (i) efficiently approximate the GED-Walk score of a given group and (ii) efficiently approximate the (proved to be $\mathcal{NP}$-hard) problem of finding a group with highest GED-Walk score. Experiments on several real-world datasets show that scores obtained by GED-Walk improve performance on common graph mining tasks such as collective classification and graph-level classification. An evaluation of empirical running times demonstrates that maximizing GED-Walk (in approximation) is two orders of magnitude faster compared to group betweenness approximation and for group sizes $\leq 100$ one to two orders faster than group closeness approximation. For graphs with tens of millions of edges, approximate GED-Walk maximization typically needs less than one minute. Furthermore, our experiments suggest that the maximization algorithms scale linearly with the size of the input graph and the size of the group.