Robustness study of hybrid hypergraphs

Recently, researchers have used the pairwise networks (lower-order) or hypergraphs (higher-order) to separately model different real systems. However, some real systems may simultaneously exist lower-order and higher-order relationships, for example, in scientist collaboration networks, there exist lower-order relationships, representing whether scientists know each other, as well as higher-order relationships, indicating shared research tasks among multiple scientists, such as co-authors of papers. In light of this, a hybrid hypergraph model that considers both lower-order and higher-order relationships is firstly considered in this work. And then, we focus on studying the robustness of hybrid hypergraphs owing to the importance of this issue. Specifically, we first introduce a collaboration efficiency (CE) metric to measure the robustness of hybrid hypergraphs. We further propose a novel edge removal strategy, termed EIHED (Edge-Included Hyperedge Efficiency Discrepancy), to study its impact on the robustness of hybrid hypergraphs. Finally, we further validate the effectiveness of our proposed strategy from both node attacking strategy and edge protection strategy.