With the success of Graph Neural Network (GNN) in network data, some GNN-based representation learning methods for networks have emerged recently. Variational Graph Autoencoder (VGAE) is a basic GNN framework for network representation. Its purpose is to well preserve the topology and node attribute information of the network to learn node representation, but it only reconstructs network topology, and doesn’t consider the reconstruction of node features. This strategy will make node representation can not well reserve node features information, impairing the ability of the VGAE method to learn higher quality representations. To solve this problem, we arise a new network representation method to improve the VGAE method for well retaining both node features and network structure information. The method utilizes adversarial mutual information learning to maximize the mutual information (MI) of node features and node representations during the encoding process of the variational autoencoder, which forces the variational encoder to get the representation containing the most informative node features. The method consists of three parts: a variational graph autoencoder includes a variational encoder(MI generator (G)) and a decoder, a positive MI sample module (maximizing MI module), and an MI discriminator(D). Furthermore, we explain why maximizing MI between node features and node representation can reconstruct node attributes. Finally, we conduct experiments on seven public representative datasets for nodes classification, nodes clustering, and graph visualization tasks. Experimental results demonstrate that the proposed algorithm significantly outperforms current popular network representation algorithms on these tasks. The best improvement is \(17.13\% \) than the VGAE method.

To address the problem that traditional spectral clustering algorithms cannot obtain the complete structural information of networks, this paper proposes a spectral clustering community detection algorithm, PMIK-SC, based on the point-wise mutual information (PMI) graph kernel. The kernel is constructed according to the point-wise mutual information between nodes, which is then used as a proximity matrix to reconstruct the network and obtain the symmetric normalized Laplacian matrix. Finally, the network is partitioned by the eigendecomposition and eigenvector clustering of the Laplacian matrix. In addition, to determine the number of clusters during spectral clustering, this paper proposes a fast algorithm, BI-CNE, for estimating the number of communities. For a specific network, the algorithm first reconstructs the original network and then runs Monte Carlo sampling to estimate the number of communities by Bayesian inference. Experimental results show that the detection speed and accuracy of the algorithm are superior to other existing algorithms for estimating the number of communities. On this basis, the spectral clustering community detection algorithm PMIK-SC also has high accuracy and stability compared with other community detection algorithms and spectral clustering algorithms.

Community structure is one of the vital characteristics of complex networks. How to effectively detect communities is a hot issue. From the perspective of information theory, the community structure of complex networks can be detected and revealed more accurately. This research introduces the average mutual information (AMI) into the detection process of the multi-label propagation algorithm (MLPA) and proposes a new community detection algorithm AMI-MLPA. The algorithm initially determines the propagation order according to the influence of nodes in the network. By selecting the label with stronger propagation intensity and smaller conditional entropy in the process of label propagation, a more reasonable community partition can be obtained. Experiments on real-world datasets and synthetic datasets show that the algorithm is better than FastGN, GN, and other LPA-based algorithms in general, with high accuracy of results on large-scale synthetic networks, which verifies the effectiveness of the algorithm.

Complex networks usually consist of dense-connected cliques, which are defined as communities. A community structure is a reflection of the local characteristics existing in the network topology, this makes community detection become an important research field to reveal the internal structural characteristics of networks. In this article, an information-based community detection approach MINC-NRL is proposed, which can be applied to both overlapping and non-overlapping community detection. MINC-NRL introduces network representation learning (NRL) to represent the target network as vectors, then generates a community evolution process based on these vectors to reduce the search space, and finally, finds the best community partition in this process using mutual information between network and communities (MINC). Experiments on real-world and synthetic data sets verifies the effectiveness of the approach in community detection, both on non-overlapping and overlapping tasks.