Distributed Algorithms for Computation of Centrality Measures in Complex Networks

TL;DR

This paper introduces distributed algorithms for computing various centrality measures in complex networks, including degree, closeness, betweenness, and PageRank, with convergence guarantees and applicability to dynamic graphs.

Contribution

It presents novel deterministic and randomized distributed algorithms that do not require network size knowledge and handle time-varying graphs, including the concept of persistent graphs.

Findings

Algorithms converge almost surely and in $L^p$ sense.

Effective in static and dynamic network scenarios.

Validated through extensive simulations on benchmark networks.

Abstract

This paper is concerned with distributed computation of several commonly used centrality measures in complex networks. In particular, we propose deterministic algorithms, which converge in finite time, for the distributed computation of the degree, closeness and betweenness centrality measures in directed graphs. Regarding eigenvector centrality, we consider the PageRank problem as its typical variant, and design distributed randomized algorithms to compute PageRank for both fixed and time-varying graphs. A key feature of the proposed algorithms is that they do not require to know the network size, which can be simultaneously estimated at every node, and that they are clock-free. To address the PageRank problem of time-varying graphs, we introduce the novel concept of persistent graph, which eliminates the effect of spamming nodes. Moreover, we prove that these algorithms converge almost surely and in the sense of $L^p$. Finally, the effectiveness of the proposed algorithms is illustrated via extensive simulations using a classical benchmark.