CHIEF: Clustering With Higher-Order Motifs in Big Networks

Abstract

Clustering network vertices is an enabler of various applications such as social computing and Internet of Things. However, challenges arise for clustering when networks increase in scale. This paper proposes CHIEF (Clustering with HIgher-ordEr motiFs), a solution which consists of two motif clustering techniques: standard acceleration CHIEF-ST and approximate acceleration CHIEF-AP. Both algorithms firstly find the maximal <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-edge-connected subgraphs within the target networks to lower the network scale by optimizing the network structure with maximal <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-edge-connected subgraphs, and then use heterogeneous four-node motifs clustering in higher-order dense networks. For CHIEF-ST, we illustrate that all target motifs will be kept after this procedure when the minimum node degree of the target motif is equal or greater than <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>. For CHIEF-AP, we prove that the eigenvalues of the adjacency matrix and the Laplacian matrix are relatively stable after this step. CHIEF offers an improved efficiency of motif clustering for big networks, and it verifies higher-order motif significance. Experiments on real and synthetic networks demonstrate that the proposed solutions outperform baseline approaches in large network analysis, and higher-order motifs outperform traditional triangle motifs in clustering.