The spread of gossip in American schools

TL;DR

This paper investigates how gossip spreads in different network structures, introduces the 'spread factor' to measure propagation, and finds that in scale-free networks, gossip spreads logarithmically with degree, with real school data confirming this pattern.

Contribution

It introduces the 'spread factor' as a new network property and analytically and empirically studies gossip propagation in scale-free and real school networks.

Findings

Gossip spreading time grows logarithmically with degree in scale-free networks.

Real school data confirms the logarithmic spreading law.

An optimal number of acquaintances minimizes gossip reach.

Abstract

We study different mechanisms of gossip propagation on several network topologies and introduce a new network property, the "spread factor", describing the fraction of neighbors that get to know the gossip. We postulate that for scale-free networks the spreading time grows logarithmically with the degree of the victim and prove this statement for the case of the Apollonian network. Applying our concepts to real data from an American school survey, we confirm the logarithmic law and disclose that there exists an ideal number of acquaintances minimizing the fraction attained by the gossip. The similarity between the school survey and scale-free networks remains even for cases when gossip propagation only occurs with some probability $q<1$. The spreading times follow an exponential distribution that can also be calculated analytically for the Apollonian network. When gossip also spreads through strangers the situation changes substantially: the spreading time becomes a constant and there exists no ideal degree of connectivity anymore.