Relay-Linking Models for Prominence and Obsolescence in Evolving Networks

Abstract: The rate at which nodes in evolving social networks acquire links (friends, citations) shows complex temporal dynamics. Preferential attachment and link copying models, while enabling elegant analysis, only capture rich-gets-richer effects, not aging and decline. Recent aging models are complex and heavily parameterized; most involve estimating 1-3 parameters per node. These parameters are intrinsic: they explain decline in terms of events in the past of the same node, and do not explain, using the network, where the linking attention might go instead. We argue that traditional characterization of linking dynamics are insufficient to judge the faithfulness of models. We propose a new temporal sketch of an evolving graph, and introduce several new characterizations of a network's temporal dynamics. Then we propose a new family of frugal aging models with no per-node parameters and only two global parameters. Our model is based on a surprising inversion or undoing of triangle completion, where an old node relays a citation to a younger follower in its immediate vicinity. Despite very few parameters, the new family of models shows remarkably better fit with real data. Before concluding, we analyze temporal signatures for various research communities yielding further insights into their comparative dynamics. To facilitate reproducible research, we shall soon make all the codes and the processed dataset available in the public domain.