Hypergraph Ego-networks and Their Temporal Evolution

TL;DR

This paper introduces hypergraph ego-networks to analyze localized higher-order interactions and proposes a deep learning-based method for their temporal reconstruction, advancing understanding of hypergraph evolution.

Contribution

It presents the concept of hypergraph ego-networks and a benchmark problem for their temporal reconstruction using a novel deep learning and hill-climbing approach.

Findings

Model effectively reconstructs hypergraph ego-networks

Combines deep learning with hill-climbing for improved accuracy

Provides a new benchmark for local hypergraph evolution prediction

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.