## 1 Introduction  
Social networks, as mappings of social relationships, have been widely studied within the framework of complex network theory. They encompass broad and profound interpersonal relationships and information exchange, covering the fields of social science and computer science, with far-reaching implications for business, politics, healthcare, and other fields [1, 2]. In complex networks, individuals are abstracted as nodes, and the relationships between nodes are abstracted as edges [3]. Social networks are characterized by many complex network features, including the small-world phenomenon [4], scale-free [5], community structure [6], and so on. Recent research has shown that an in-depth exploration of the characteristics of the community structure of social networks is helpful to reveal the intrinsic organization and patterns of networks in community structures [7]. In this way, it provides strong theoretical support for a more comprehensive understanding of the structure and function of social networks. In recent years, social network structure optimization methods have been classified into global optimization algorithms and local optimization algorithms based on the scope of their search space and the nature of their objectives. In the 20 th century, [PERSON] et al. [8] proposed the Kernighan-Lin algorithm, which partitions the network into predefinedsizes and quantities, defining a function gain for network partitioning and dividing the community based on the change in gain. A large variety of global optimization algorithms evolved from this idea. [PERSON] (1986) defines edge betweenness as the importance index of edges, and they sequentially remove non-community core edges from the network to obtain the community partitioning result; in contrast, [PERSON] et al. [PERSON] et al. (2010) propose a merging clustering algorithm to add edges to the network sequentially based on maximal clusters. [PERSON] et al. [PERSON] (1986) first proposed a modular function to measure the results of community division in 2004, and since then a lot of optimization algorithms have been proposed and improved based on modular functions. [PERSON] et al. [PERSON] et al. (2011) optimize the modular function Q using the fitness value of genetic algorithms; [PERSON] et al. [PERSON] et al. (2012) present an extreme optimization semi-supervised algorithm based on pairwise constraint structure enhancement, which solved the pseudo-connection problem. However, the modularity optimization algorithm is an NP-complete problem, and it is difficult to find the optimal solution in polynomial time. [PERSON] et al. [PERSON] et al. (2013) first introduced the concept of spectral clustering, and in the same year, [PERSON] et al. [PERSON] et al. (2014) extended spectral clustering to community detection technology by using the Laplace matrix. [PERSON] et al. [PERSON] et al. (2015) and [PERSON] et al. [PERSON] et al. (2016) use the normalized Laplacian matrix to define the spectral clustering algorithm to achieve processing of large datasets under sparse similarity graph constraints. However, each of these global optimization algorithms has obvious limitations in application by requiring information about the topology of the entire network, as well as the number and size of predefined communities. Later, [PERSON] et al. [PERSON] et al. (2017) proposed a local optimization algorithm, which led to the emergence of various local optimization algorithms such as the clique percolation method [PERSON] et al. (2018), the label propagation algorithm [PERSON] et al. (2018), and the local edge clustering optimization algorithm [PERSON] et al. (2018). The traditional label propagation algorithm [PERSON] et al. (2018) is an efficient local optimization algorithm that does not require complete network structure information and has lower time complexity, which is close to linear complexity, but the algorithm is highly random and weakly robust and is prone to fall into local optima, which makes it difficult to obtain effective community detection.