Rumours spread slowly in a small world spatial network

TL;DR

This paper investigates the spread of rumours in a spatial network model, showing that despite small-world properties, rumour dissemination remains slow and polynomial in network size.

Contribution

It demonstrates that in the SPA model, small effective diameter does not lead to rapid rumour spreading, revealing a discrepancy between network structure and information diffusion.

Findings

SPA graphs have small effective diameter, O(log^2 n)

Rumour spreading is polynomial in n, indicating slow dissemination

Small-world structure does not guarantee fast information spread

Abstract

Rumour spreading is a protocol for modelling the spread of information through a network via user-to-user interaction. The Spatial Preferred Attachment (SPA) model is a random graph model for complex networks: vertices are placed in a metric space, and the link probability depends on the metric distance between vertices, and on their degree. We show that the SPA model typically produces graphs that have small effective diameter, i.e. $O(\log^2 n)$, while rumour spreading is relatively slow, namely polynomial in $n$.