Aqua­chlorido{6,6′-dimeth­oxy-2,2′-[ethane-1,2-diylbis(nitrilo­dimethyl­idyne)]diphenolato-κ2 O 1,N,N′,O 1′}cobalt(III) monohydrate

The title compound, [Co(C18H18N2O4)Cl(H2O)]·H2O, contains a distorted octa­hedral cobalt(III) complex with a 6,6′-dimeth­oxy-2,2′-[ethane-1,2-diylbis(nitrilo­dimethyl­idyne)]diphenolate ligand, a chloride and an aqua ligand, and also a disordered water solvent mol­ecule (half-occupancy). The CoIII ion is coordinated in an N2O3Cl manner. Weak O—H⋯O hydrogen bonds may help to stabilize the crystal packing

CHIEF : clustering With higher-order motifs in big networks

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 $k$-edge-connected subgraphs within the target networks to lower the network scale by optimizing the network structure with maximal $k$-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 $k$. 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. © 2022 IEEE Computer Society. All rights reserved

CHIEF: Clustering with Higher-order Motifs in Big Networks

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