Hypergraph Ego-networks and Their Temporal Evolution (2112.03498v1)

Abstract: Interactions involving multiple objects simultaneously are ubiquitous across many domains. The systems these interactions inhabit can be modelled using hypergraphs, a generalization of traditional graphs in which each edge can connect any number of nodes. Analyzing the global and static properties of these hypergraphs has led to a plethora of novel findings regarding how these modelled systems are structured. However, less is known about the localized structure of these systems and how they evolve over time. In this paper, we propose the study of hypergraph ego-networks, a structure that can be used to model higher-order interactions involving a single node. We also propose the temporal reconstruction of hypergraph ego-networks as a benchmark problem for models that aim to predict the local temporal structure of hypergraphs. By combining a deep learning binary classifier with a hill-climbing algorithm, we will present a model for reconstructing hypergraph ego-networks by incorporating structural patterns found across multiple domains.