GHOC: A generative model for hybrid‐order community detection

Abstract

Recently, hybrid-order community detection has been proposed for addressing the hypergraph fragmentation issue suffered by the motif-based higher-order community detection. However, the existing attempts of hybrid-order community detection inadvertently damage the lower-order connectivity pattern and the higher-order connectivity pattern when constructing the fusion model. Additionally, like the higher-order community detection approaches, they also adopt a two-phase strategy that separately applies the existing graph node clustering methods to the proximity matrix derived from the lower-order connectivity pattern and the higher-order connectivity pattern. Therefore, the higher-order connectivity pattern is only utilized for constructing proximity matrix and hence has no direct effect on the final community results. In this paper, to address the above issues, we propose a Generative model for Hybrid-Order Community detection (GHOC). The main idea lies in defining a likelihood function of a generative model that finds the optimal community membership strength vectors of nodes, based on which the original lower-order connectivity pattern and the higher-order connectivity pattern can be directly reconstructed simultaneously. From the community membership strength vectors, the final community structure can be derived. Extensive

Community detection from fuzzy and higher-order perspectives

“…-Higherorder community detection (HCD) is defined as community detection based on higher-order connectivity patterns (e.g., motif [19]). Network motifs are considered as the basic building blocks and functional units of complex networks [20][21][22], which contain deeper community signatures than edges and reflect specific functionalities [8]. In a higher-order community partition based on motifs, a community is defined as a cluster of nodes that preserves as many instances of motif as possible and avoids cutting any instances of motif [12].…”

“…Higher-order community detection (HCD) can reveal network organizational rules at the level of higher-order connectivity patterns (e.g., network motifs [19]), providing a new perspective for mesoscale topological analysis of complex networks [12]. Network motifs are considered as fundamental building blocks and functional units of complex networks [20][21][22], which can better characterize the existence of communities than classical lower-order connectivity patterns (e.g., edges) [8]. Specifically, HCD can find node clusters more accurately based on specific network motifs [23], and the nodes in each cluster participate in as many motif instances as possible, avoiding cutting any motif instance [12].…”