Rumors in a Network: Who's the Culprit?

TL;DR

This paper introduces a novel estimator called rumor centrality for identifying the source of a rumor in various network types, demonstrating its effectiveness through theoretical analysis and simulations.

Contribution

It proposes rumor centrality as a new topological measure for rumor source detection and establishes its optimality as an ML estimator on certain graphs.

Findings

Estimator has non-trivial detection probability on fast-growing trees.

Detection probability approaches zero on line-like trees as network grows.

Rumor centrality outperforms distance centrality in non-tree networks.

Abstract

We provide a systematic study of the problem of finding the source of a rumor in a network. We model rumor spreading in a network with a variant of the popular SIR model and then construct an estimator for the rumor source. This estimator is based upon a novel topological quantity which we term \textbf{rumor centrality}. We establish that this is an ML estimator for a class of graphs. We find the following surprising threshold phenomenon: on trees which grow faster than a line, the estimator always has non-trivial detection probability, whereas on trees that grow like a line, the detection probability will go to 0 as the network grows. Simulations performed on synthetic networks such as the popular small-world and scale-free networks, and on real networks such as an internet AS network and the U.S. electric power grid network, show that the estimator either finds the source exactly or within a few hops of the true source across different network topologies. We compare rumor centrality to another common network centrality notion known as distance centrality. We prove that on trees, the rumor center and distance center are equivalent, but on general networks, they may differ. Indeed, simulations show that rumor centrality outperforms distance centrality in finding rumor sources in networks which are not tree-like.