The spread of gossip in American schools

Gossip is defined as a rumor which specifically targets one individual and essentially only propagates within its friendship connections. How fast and how far a gossip can spread is for the first time assessed quantitatively in this study. For that purpose we introduce the “spread factor” and study it on empirical networks of school friendships as well as on various models for social connections. We discover that there exists an ideal number of friendship connections an individual should have to minimize the danger of gossip propagation. Copyright c © EPLA, 2007 Introduction. – Gossip is so inherent to human nature that it was already worshiped in the Greek mythology through the many-tongued Pheme. Its impact in history and in sociology is so large that it has been studied from many points of view [1,2]. However, recent insights into the mathematical properties of social networks [3,4] and particularly those involving friendships [5], open up a new way of understanding how the propagation of gossip depends on connections of friendships. We will in particular consider gossip within the society of American school students. In the last years many social network models have been studied serving to describe phenomena ranging from the Internet, epidemics and rumor spreading to scientific collaborations, movie actors and sexual intercourse [3–8]. Many properties have been identified to characterize these networks like the degree distribution, the shortest path, the cliquishness, the inbetweenness, etc. The study of gossip propagation, however, requires still another up to now never considered analysis, giving rise to what we call the “spread factor” and the “spreading time” which we will introduce in this letter and discuss their properties and applications. Using these properties we will present a striking finding: in real social systems there is the possibility to minimize the risk of being gossiped, by choosing an optimal number of friendship connections. A simple model for gossip propagation. – As opposed to rumors, a gossip targets the behavior or private life of a specific person, i.e., a target node (victim) in the network. To model the social network we consider that individuals are vertices connected by bonds representing their friendship connections as illustrated in fig. 1. At time t= 0 a gossip (be it truth or falsehood) is created about the victim by the “originator” (grey face). In the normal case the gossip is only of interest to those who know the victim personally and we therefore consider that it only spreads at each time step from the vertices that know the gossip to all vertices that are connected to the victim and do not yet know the gossip, i.e. over the arrows in fig. 1. Our dynamics is therefore similar to an epidemics or a burning algorithm [9], starting at the originator but limited to sites that are neighbors of the victim. The gossip spreads until attaining all reachable connections of the victim, i.e. after three time steps in fig. 1. To measure how effectively the gossip attains the friends of the victim, we calculate the total number nf of friends (nearest neighbors) who eventually hear the gossip in a network with N vertices (individuals), and the minimum time τ it takes to attain the accessible friends, which we call the “spreading time”. We define the “spread factor” as the fraction of attained nearest