Random Information Spread in Networks

TL;DR

This paper investigates the process of information spreading in networks, establishing a link with stochastic shortest paths, analyzing special graph cases, and proposing bounds for expected arrival times.

Contribution

It introduces an equivalence between expected first arrival times in information spread and stochastic shortest paths, with analysis on specific graph types and bounds.

Findings

Expected s-t first arrival time linked to stochastic shortest path

Analytical results for complete and series-parallel graphs

Lower bounds for expected arrival times proposed

Abstract

Let G=(V,E) be an undirected loopless graph with possible parallel edges and s and t be two vertices of G. Assume that vertex s is labelled at the initial time step and that every labelled vertex copies its labelling to neighbouring vertices along edges with one labelled endpoint independently with probability p in one time step. In this paper, we establish the equivalence between the expected s-t first arrival time of the above spread process and the notion of the stochastic shortest s-t path. Moreover, we give a short discussion of analytical results on special graphs including the complete graph and s-t series-parallel graphs. Finally, we propose some lower bounds for the expected s-t first arrival time.