Hyperedge Entanglement in High-Order Multilayer Networks

Abstract

Many real complex systems present multilayer structure where high-order metadata on one layer refers to dyadic data on a lower layer. Significant progresses to analyse high-order metadata under the assumption of community organization have been done. However, there are no planted communities in real-world networks, and the necessity of new frameworks to analyze high-order metadata regardless of community organization has been raised.Here, we propose to adopt hyperedge organization. Predicting ‘entanglements’ between a hyperedge and nodes scattered in the rest of the network might suggest structural or functional liaisons, without assumption of any community organization. We introduce a novel concept: hyperedge entanglement (HE), which associates to each hyperedge an entangled hyperedge, by means of a network operator that predicts significant ‘interactions at distance’ between network nodes and existing hyperedges. We also introduce a new challenge termed hyperedge entanglement prediction (HEP), and an algorithm to perform this task. We evaluated HEP performance on social, biological and synthetic data where, given only topology and hyperedges (such as communities or functional modules), the goal is to predict whether nodes not connected to a certain hyperedge might be candidates for a significant entanglement. Finally, as real application in diseasome systems biomedicine, we perform HEP on the human protein interactome to predict unknown gene entanglements with the COPD disease gene hyperedge. HEP predictions are validated by biological experiments, enlarging our understanding of molecular mechanisms behind COPD/aneurysm comorbidity.

Experimental analyses on 2-hop-based and 3-hop-based link prediction algorithms

“…The degree of node i is denoted by k i and the set of neighbors of node i is denoted by Γ i . Four representative 2-hop-based indices, CN [14], RA [15,38], AA [25], and CH2 [26,37], as well as their 3-hop-based counterparts are considered in this paper.…”

“…CH2-L2 index [37] rewards internal links among common neighbors while penalizes links connecting common neighbors and outside. The similarity between nodes i and j is…”

“…Indeed, which index is the best choice largely depends on the specific structure of the target network. An unexpected gain from these experiments is that the class of CH2 indices [37] perform the best among all 4 classes with a dominant winning 62.65%, and the class of RA indices [15] is the runner-up with a winning rate 24.15%, while the other two classes perform poorly, with both winning rates being about 7%. Figure 4 validates the robustness of the above experimental results by varying the ratio q.…”

“…Very recently, some scientists have argued that 3-hop-based similarity indices perform better than 2-hop-based indices [35][36][37]. For example, Kovács et al [36] proposed a degree-normalized index based on 3-hop paths and showed its remarkable advantage compared with 2-hop-based indices in predicting proteinprotein interactions.…”

“…However, given a specific target network, which index is the best choice still largely depends on the network structure. Overall speaking, the class of Cannistraci-Hebb (CH) indices [37] performs the best among all considered candidates, and the class of resource allocation (RA) indices [15] is the runner-up.…”