February 6, 2013

Arrival and Departure Dynamics in Social Networks

ACM International Conference on Web Search and Data Mining (WSDM)

By: Shaomei Wu, Atish Das Sarma, Alex Fabrikant, Silvio Lattanzi, Andrew Tomkins

Abstract

In this paper, we consider the natural arrival and departure of users in a social network, and ask whether the dynamics of arrival, which have been studied in some depth, also explain the dynamics of departure, which are not as well studied.

Through study of the DBLP co-authorship network and a large online social network, we show that the dynamics of departure behave differently from the dynamics of formation. In particular, the probability of departure of a user with few friends may be understood most accurately as a function of the raw number of friends who are active. For users with more friends, however, the probability of departure is best predicted by the overall fraction of the user’s neighborhood that is active, independent of size.

We then study global properties of the subgraphs induced by active and inactive users, and show that active users tend to belong to a core that is densifying and is significantly denser than the inactive users. Further, the inactive set of users exhibit a higher density and lower conductance than the degree distribution alone can explain. These two aspects suggest that nodes at the fringe are more likely to depart and subsequent departures are correlated among neighboring nodes in tightly-knit communities.