Community structure is a very interesting attribute and feature in complex networks, which has attracted scholars’ attention and research on community detection. Many single-objective optimization algorithms have been migrated and modified to serve community detection problems. Due to the limitation of resolution, the final algorithm implementation effect is not ideal. In this paper, a multi-objective community detection method based on a pigeon-inspired optimization algorithm, MOPIO-Net, is proposed. Firstly, the PIO algorithm is discretized in terms of the solution space representation, position, and velocity-updating strategies to adapt to discrete community detection scenarios. Secondly, by minimizing the two objective functions of community score and community fitness at the same time, the community structure with a tight interior and sparse exterior is obtained. Finally, for the misclassification caused by boundary nodes, a mutation strategy is added to improve the accuracy of the final community recognition. Experiments on synthetic and real networks verify that the proposed algorithm is more accurate in community recognition compared to 11 benchmark algorithms, confirming the effectiveness of the proposed method.

There are many evolving dynamic networks in the real world, and community detection in dynamic networks is crucial in many complex network analysis applications. In this paper, a consensus community-based discrete spider wasp optimization (SWO) approach is proposed for the dynamic network community detection problem. First, the coding, initialization, and updating strategies of the spider wasp optimization algorithm are discretized to adapt to the community detection problem. Second, the concept of intra-population and inter-population consensus community is proposed. Consensus community is the knowledge formed by the swarm summarizing the current state as well as the past history. By maintaining certain inter-population consensus community during the evolutionary process, the population in the current time window can evolve in a similar direction to those in the previous time step. Experimental results on many artificial and real dynamic networks show that the proposed method produces more accurate and robust results than current methods.

In network science, identifying key nodes is crucial for understanding and optimizing the structure and functionality of complex networks. The traditional K-shell decomposition method has limitations in revealing the core structure of networks, often overlooking the interactions among nodes and the global characteristics of the network. This study proposes an improved K-shell algorithm that incorporates the concept of "Neighbor Degree Sum" to differentiate nodes with the same k-value more finely and assess node importance more accurately. By considering both the connectivity of the nodes and their neighbors, the algorithm achieves a more nuanced stratification, enhancing the precision of key node identification. Validation on social network datasets demonstrates that this algorithm outperforms traditional methods in effectively identifying key nodes, deepening our understanding of the mechanisms behind key node identification in complex networks, and providing new tools for fields such as social network analysis, internet maintenance, and traffic optimization.