To stay or not to stay: modeling engagement dynamics in social graphs

Given a large social graph, how can we model the engagement properties of nodes? Can we quantify engagement both at node level as well as at graph level? Typically, engagement refers to the degree that an individual participates (or is encouraged to participate) in a community and is closely related to the important property of nodes' departure dynamics, i.e., the tendency of individuals to leave the community. In this paper, we build upon recent work in the field of game theory, where the behavior of individuals (nodes) is modeled by a technology adoption game. That is, the decision of a node to remain engaged in the graph is affected by the decision of its neighbors, and the "best practice" for each individual is captured by its core number - as arises from the k-core decomposition. After modeling and defining the engagement dynamics at node and graph level, we examine whether they depend on structural and topological features of the graph. We perform experiments on a multitude of real graphs, observing interesting connections with other graph characteristics, as well as a clear deviation from the corresponding behavior of random graphs. Furthermore, similar to the well known results about the robustness of real graphs under random and targeted node removals, we discuss the implications of our findings on a special case of robustness - regarding random and targeted node departures based on their engagement level.