Computing Classic Closeness Centrality, at Scale

TL;DR

This paper introduces a highly scalable algorithm for estimating classic closeness centrality in large networks, achieving near linear time and small error margins, applicable to both undirected and directed graphs.

Contribution

It presents the first near linear-time algorithm for approximating classic closeness centrality with high accuracy and scalability, including extensions for directed graphs.

Findings

Algorithm achieves near linear time complexity.

High accuracy in estimating closeness centrality.

Effective on large real-world networks.

Abstract

Closeness centrality, first considered by Bavelas (1948), is an importance measure of a node in a network which is based on the distances from the node to all other nodes. The classic definition, proposed by Bavelas (1950), Beauchamp (1965), and Sabidussi (1966), is (the inverse of) the average distance to all other nodes. We propose the first highly scalable (near linear-time processing and linear space overhead) algorithm for estimating, within a small relative error, the classic closeness centralities of all nodes in the graph. Our algorithm applies to undirected graphs, as well as for centrality computed with respect to round-trip distances in directed graphs. For directed graphs, we also propose an efficient algorithm that approximates generalizations of classic closeness centrality to outbound and inbound centralities. Although it does not provide worst-case theoretical approximation guarantees, it is designed to perform well on real networks. We perform extensive experiments on large networks, demonstrating high scalability and accuracy.