Community Detection with Higher-Order Edge Enhancement in Temporal Networks

Abstract Dynamic community detection often suffers from the instability of results, making consistent community identification across network snapshots critically important. However, the cut off between snapshots might lead to the loss of some higher-order structures, such as closed triangle motifs. In view of this, we examine the relationship between the missing higher-order structures and the instability, and find a positive correlation between higher-order loss ratio (HOLR) and temporal smoothing normalized mutual information (TSNMI). Based on this finding, we propose a new-brand higher-order edge enhancement (HOEE) algorithm, aiming to effectively reconstruct higher-order interactions to overcome the instability issue. The HOEE algorithm employs the higher-order activity potential (HAP) of nodes between consecutive snapshots to recover the loss of higher-order information by the transformation of the triangle motif, thus ensuring the temporal stability of dynamic communities. Experimental evaluation on synthetic and real-world dynamic networks demonstrates that HOEE outperforms state-of-the-art methods in community detection accuracy and significantly reduces community instability. Theoretical analysis confirms stability guarantees and characterizes graph property changes induced by HOEE. The HOEE algorithm effectively enhances temporal community stability through higher-order interaction reconstruction, providing a robust solution for dynamic network analysis.