The spread of gossip in American schools

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.