Community structure is one of the important characteristics of complex networks. Community discovery or detection has important theoretical significance and practical value. At present, estimation of the number of communities (or clusters) is still an open question. By Bayesian inference, this research deduces the relationship between maximum possible partition and mutual information and information entropy, and proposes a framework algorithm Clustering Number Estimation (CNE) and a concrete implementation to estimate the number of clusters (K). Several typical algorithms for community number estimation are compared on several typical data sets, and primary experiments validate the effectiveness of this method.

Representation learning on networks, mapping the network into a low-dimensional vector space, has received signification attention recently due to its widespread application in graph data mining tasks. With the success of representation learning in static networks, we push further for practical scenarios of dynamic networks. Existing methods model the dynamic network by dividing the dynamic network into sequences of network snapshots, see each network snapshot as a static network, and utilize the dynamic evolution between snapshots, they capture the discrete dynamic evolution of dynamic networks. However, a dynamic network continuously evolves over time. Capturing the continuously dynamic evolution of dynamic networks is important for dynamic network representation. In this article, we regard a dynamic network as a dynamic system, use the ordinary differential equation (ODE) to model the dynamic evolution of dynamic networks, and integrate the ODE over continuous-time to capture continuously dynamic evolution of dynamic networks; and design a new encoder-decoder model for dynamic networks representation. We improve the gated recurrent unit (GRU) module (only capturing the discrete dynamic evolution of the dynamic network and structure information) by combining an ODE and a GRU. The improved GRU as the encoder can learn the continuously dynamic evolution, and structure information of the dynamic network, where the ODE parameterized by a graph neural network models the continuously dynamic evolution of each network snapshot. Use the ODE and Inner-Productor as the decoder, where the ODE is integrated over continuous-time to learn the continuous dynamic evolution of the latent representation of the whole dynamic network, and the Inner-Productor reconstructs the topological structure of each snapshot by doing the inner-product between nodes representation, the reconstructing errors as the objective function of our method. To assess our model, we expand the experiment on several real-world dynamic networks, and results show that our method consistently outperforms existing baselines in three dynamic link prediction tasks; the best is up to 6.54 \( % \) improvement. To our knowledge, our method is the first work using the ODE to capture the continuously dynamic evolution of dynamic networks.

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 does not 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.

Community detection is one of the most important contents of complex network research, and it faces the challenge of balancing accuracy and efficiency. In response to this challenge, the paper proposes a community detection algorithm based on feature propagation. The algorithm first randomly initializes a vector for each node of the graph to complete the feature initialization. Then, with the help of the node similarity matrix, the vector representation of each node in the graph is learned through feature propagation, and finally the K-means clustering algorithm is used to cluster to obtain the community detection result. We have conducted experiments on real datasets and LFR datasets with the metric of NMI, and the results show that our algorithm is accurate and efficient.