  Clustering a group of vertices in networks facilitates applications across
different domains, such as social computing and Internet of Things. However,
challenges arises for clustering networks with increased scale. This paper
proposes a solution which consists of two motif clustering techniques: standard
acceleration CHIEF-ST and approximate acceleration CHIEF-AP. Both algorithms
first find the maximal k-edge-connected subgraphs within the target networks to
lower the network scale, then employ higher-order motifs in clustering. In the
first procedure, we propose to lower the network scale by optimizing the
network structure with maximal k-edge-connected subgraphs. 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 k. For
CHIEF-AP, we prove that the eigenvalues of the adjacency matrix and the
Laplacian matrix are relatively stable after this step. That is, CHIEF-ST has
no influence on motif clustering, whereas CHIEF-AP introduces limited yet
acceptable impact. In the second procedure, we employ higher-order motifs,
i.e., heterogeneous four-node motifs clustering in higher-order dense networks.
The contributions of CHIEF are two-fold: (1) improved efficiency of motif
clustering for big networks; (2) verification of higher-order motif
significance. The proposed solutions are found to outperform baseline
approaches according to experiments on real and synthetic networks, which
demonstrates CHIEF's strength in large network analysis. Meanwhile,
higher-order motifs are proved to perform better than traditional triangle
motifs in clustering.
