Improved local search algorithm for community detection in higher-order networks and its applications

With the widespread application of complex networks in both natural and social systems, higher-order structural characteristics of multi-node interactions have become increasingly prominent. Higher-order network community detection effectively captures collaborative topological features among multiple nodes, revealing system functional modules and dynamic evolution patterns that traditional methods often struggle to identify. Existing community detection algorithms that rely on complete network data face challenges related to efficiency and partitioning quality. These limitations restrict their adaptability to complex real-world scenarios. This study proposes an enhanced approach by constructing a weighted higher-order network based on triangle motifs, which effectively represents triadic collaborations. We introduce a weighted average position strategy into the Local Search (LS) algorithm, thereby improving search precision through an analysis of node significance and connection weights. To mitigate the issue of local optima entrapment, we implement a probabilistic selection mechanism that balances local and global exploration. Experimental validation on benchmark networks demonstrates significant improvements in modularity, normalized mutual information, and F1-score. When applied to real-world credit card networks, our method achieves accurate customer community division, providing novel insights for the financial applications of higher-order network analysis.