Overlapping community detection with least replicas in complex networks

In the context of network theory, overlapping community detection finds communities with certain nodes belonging to multiple communities. In recent decades, many such algorithms have been proposed but suffer from the following limitations: (1) high computational complexity, which limits the applicability of most algorithms in large-scale networks; (2) highly overlapped communities with too many overlapping nodes, which might cause communities to lack unique features because they share many nodes; (3) low steadiness, which means that the divisions found by selected algorithms might differ from time to time; and (4) unidentified nodes, which means a failure to classify every node into communities. To avoid such problems, we propose a novel algorithm in this paper for overlapping community detection with least replicas, i.e., OCDLR. More specifically, first, the algorithm defines the edge intensity to quantify the relationship between each pair of connected nodes, where a higher intensity means closer relationship. Second, the algorithm extracts edges with intensities above a given threshold as skeleton edges and specifies the nodes of skeleton edges as core nodes and others as margin nodes. Third, the process identifies all potential overlapping nodes from the core node set and optimally replicates them, ensuring that replicas remain as far apart as possible but still belong to the core node set. By applying the congregating strategy twice, the algorithm combines different groups of core nodes that are connected by skeleton edges as disjoint initial communities and attaches margin nodes to the nearest communities. The replicas of the same original node that belong to the same community are reassembled as one, and after such adjustments, the number of replicas are minimized, and overlapping communities with the least replicas can be acquired. Experimental results on real networks show the efficiency and accuracy of our method.