Finding Rumor Sources on Random Trees
Devavrat Shah, Tauhid Zaman

TL;DR
This paper proves the effectiveness of rumor centrality for source detection in generic random trees and SI models with arbitrary spreading times, extending previous results and establishing universality in tree-like graphs.
Contribution
It establishes the effectiveness of rumor centrality for source detection in general random trees and SI models with arbitrary spreading times, using a novel connection to continuous time branching processes.
Findings
Rumor centrality is effective for source detection in generic random trees.
The detection probability can be precisely quantified.
Universality of rumor centrality in tree-like graphs is demonstrated.
Abstract
We consider the problem of detecting the source of a rumor which has spread in a network using only observations about which set of nodes are infected with the rumor and with no information as to \emph{when} these nodes became infected. In a recent work \citep{ref:rc} this rumor source detection problem was introduced and studied. The authors proposed the graph score function {\em rumor centrality} as an estimator for detecting the source. They establish it to be the maximum likelihood estimator with respect to the popular Susceptible Infected (SI) model with exponential spreading times for regular trees. They showed that as the size of the infected graph increases, for a path graph (2-regular tree), the probability of source detection goes to while for -regular trees with the probability of detection, say , remains bounded away from and is less than…
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Taxonomy
TopicsComplex Network Analysis Techniques · Opinion Dynamics and Social Influence · Opportunistic and Delay-Tolerant Networks
