Are k-cores meaningful for temporal graph analysis?

Communities and dense substructures are one of the fundamental concepts in graph analysis, and the k-core is one of the most widely used models for its simplicity and effectiveness. As temporal graphs become more commonly available and larger, the algorithmic community is taking the fundamentals of static graph analysis and defining parallel concepts on temporal graphs. These adaptations, however, seem to follow the goal of being intuitive and concise, but there is yet to be a study showing whether they actually capture useful information in real temporal graphs.This is precisely what we aim to do in this paper: we look at several proposed definitions for the temporal k-core, aiming to assess whether their effectiveness matches that of the static counterpart.First, we unify several existing definitions of temporal k-core with a convenient general notation, and show a simple data structure to compute them efficiently. Then, taking inspiration from static graph analysis, we devise meaningful ways to aggregate and visualize information obtained from temporal k-cores: we show that indeed, temporal k-cores do uncover significant insights on both nodes and the dynamics of the network as a whole, which are not observable with static graph analysis.