Link prediction is one of the most important and challenging tasks in complex network analysis, which aims to predict the existence of unknown links based on the known information in the network. As critical topological properties in the network, node’s degree and clustering coefficient are well-suited for describing the tightness of connection between nodes. The importance of node can affect the possibility of link existence to a certain extent. By analyzing the impact of different centrality on links, which concluded that the degree centrality and proximity centrality have the greatest influence on network link prediction. A link prediction algorithm combines importance of node and network topological properties, called DCCLP, is proposed in this paper, the symmetry of the adjacency matrix is considered in the DCCLP link prediction algorithm to further describe the structural similarity of network nodes. In the training phase of the DCCLP algorithm, the maximized AUC indicator in the training set as the objective, and the optimal parameters are estimated by utilizing the White Shark Optimization algorithm. Then the prediction accuracy of the DCCLP algorithm is evaluated in the test set. By experimenting on twenty-one networks with different scales, and comparing with existing algorithms, the experimental results show that the effectiveness and feasibility of DCCLP algorithm, and further illustrate the importance of the degree centrality of node pairs and proximity centrality of nodes to improve the prediction accuracy of link prediction.

To balance the diversity and stringency of Pareto solutions in multi-objective optimization, this paper introduces a multi-objective White Shark Optimization algorithm (MONSWSO) tailored for multi-objective optimization. MONSWSO integrates non-dominated sorting and crowding distance into the White Shark Optimization framework to select the optimal solution within the population. The uniformity of the initial population is enhanced through a chaotic reverse initialization learning strategy. The adaptive updating of individual positions is facilitated by an elite-guided forgetting mechanism, which incorporates escape energy and eddy aggregation behavior inspired by marine organisms to improve exploration in key areas. To evaluate the effectiveness of MONSWSO, it is benchmarked against five state-of-the-art multi-objective algorithms using four metrics: inverse generation distance, spatial homogeneity, spatial distribution, and hypervolume on 27 typical problems, including 23 multi-objective functions and 4 multi-objective project examples. Furthermore, the practical application of MONSWSO is demonstrated through an example of optimizing the design of subway tunnel foundation pits. The comprehensive results reveal that MONSWSO outperforms the comparison algorithms, achieving impressive and satisfactory outcomes.

An interactive artificial ecological optimization algorithm (SIAEO) based on environmental stimulus and a competition mechanism was devised to find the solution to a complex calculation, which can often become bogged down in local optimum because of the sequential execution of consumption and decomposition stages in the artificial ecological optimization algorithm. Firstly, the environmental stimulus defined by population diversity makes the population interactively execute the consumption operator and decomposition operator to abate the inhomogeneity of the algorithm. Secondly, the three different types of predation modes in the consumption stage were regarded as three different tasks, and the task execution mode was determined by the maximum cumulative success rate of each individual task execution. Furthermore, the biological competition operator is recommended to modify the regeneration strategy so that the SIAEO algorithm can provide consideration to the exploitation in the exploration stage, break the equal probability execution mode of the AEO, and promote the competition among operators. Finally, the stochastic mean suppression alternation exploitation problem is introduced in the later exploitation process of the algorithm, which can tremendously heighten the SIAEO algorithm to run away the local optimum. A comparison between SIAEO and other improved algorithms is performed on the CEC2017 and CEC2019 test set.

Community detection is an important content in complex network analysis. The existing community detection methods in attributed networks mostly focus on only using network structure, while the methods of integrating node attributes is mainly for the traditional community structures, and cannot detect multipartite structures and mixture structures in network. In addition, the model-based community detection methods currently proposed for attributed networks do not fully consider unique topology information of nodes, such as betweenness centrality and clustering coefficient. Therefore, a stochastic block model that integrates betweenness centrality and clustering coefficient of nodes for community detection in attributed networks, named BCSBM, is proposed in this paper. Different from other generative models for attributed networks, the generation process of links and attributes in BCSBM model follows the Poisson distribution, and the probability between community is considered based on the stochastic block model. Moreover, the betweenness centrality and clustering coefficient of nodes are introduced into the process of links and attributes generation. Finally, the expectation maximization algorithm is employed to estimate the parameters of the BCSBM model, and the node-community memberships is obtained through the hard division process, so the community detection is completed. By experimenting on six real-work networks containing different network structures, and comparing with the community detection results of five algorithms, the experimental results show that the BCSBM model not only inherits the advantages of the stochastic block model and can detect various network structures, but also has good data fitting ability due to introducing the betweenness centrality and clustering coefficient of nodes. Overall, the performance of this model is superior to other five compared algorithms.

Link prediction is one of the most important and challenging tasks in complex network analysis, which aims to predict the likelihood of the existence of missing links based on the known information in the network. As critical topological properties in the network, node degree and clustering coefficient are well-suited for describing the tightness of connection between nodes. The node importance can affect the possibility of link existence to a certain extent. By analyzing the impact of different centrality on links, which concluded that the degree centrality and proximity centrality have the greatest influence on link prediction. So, a link prediction algorithm combines node importance and attribute, called DCCLP, is proposed in this paper. In the training phase of the DCCLP algorithm, the maximized AUC indicator in the training set as the objective, and the optimal parameters are estimated by utilizing the White Shark Optimization algorithm. Then the prediction accuracy of the DCCLP algorithm is evaluated in the test set. By experimenting on twenty-one networks with different scales, and comparing with existing algorithms, the experimental results show that the effectiveness and feasibility of DCCLP algorithm, and further illustrate the importance of the degree centrality of node pairs and proximity centrality of nodes to improve the prediction accuracy of link prediction.