Computing Top-k Closeness Centrality in Fully-dynamic Graphs

TL;DR

This paper introduces efficient dynamic algorithms for maintaining the top-k nodes with highest closeness centrality in evolving networks, significantly outperforming static recomputation methods.

Contribution

It presents novel algorithms for dynamic top-k closeness centrality computation that leverage previous computations to improve efficiency without extra asymptotic memory costs.

Findings

Dynamic algorithms are up to 10,000 times faster than static recomputation.

Algorithms perform well on various real-world networks, including small-world and large-diameter graphs.

Significant speedups are achieved after edge updates in evolving networks.

Abstract

Closeness is a widely-studied centrality measure. Since it requires all pairwise distances, computing closeness for all nodes is infeasible for large real-world networks. However, for many applications, it is only necessary to find the k most central nodes and not all closeness values. Prior work has shown that computing the top-k nodes with highest closeness can be done much faster than computing closeness for all nodes in real-world networks. However, for networks that evolve over time, no dynamic top-k closeness algorithm exists that improves on static recomputation. In this paper, we present several techniques that allow us to efficiently compute the k nodes with highest (harmonic) closeness after an edge insertion or an edge deletion. Our algorithms use information obtained during earlier computations to omit unnecessary work. However, they do not require asymptotically more memory than the static algorithms (i. e., linear in the number of nodes). We propose separate algorithms for complex networks (which exhibit the small-world property) and networks with large diameter such as street networks, and we compare them against static recomputation on a variety of real-world networks. On many instances, our dynamic algorithms are two orders of magnitude faster than recomputation; on some large graphs, we even reach average speedups between $10^3$ and $10^4$.