Allison Shaw, Roozbeh Daneshvar, and I developed a simple model for the effect of gossip spread on social network structure. We define gossip as information passed between two individuals A and B about a third individual C which affects the strengths of all three relationships: it strengthens A-B and weakens both B-C and A-C. We found, in both an analytic derivation and model simulations, that if gossip does not spread beyond simple triads, it destroys them but if gossip propagates through large dense clusters, it strengthens them. Additionally, our simulations showed that the effect of gossip on network metrics (clustering coefficient, average path length, and the sum of strengths) varies with network structure and average node degree.

The paper can be found here.