Graphlet-Based Edge Weighting for Improved Community Detection in Complex Networks

Abstract Community detection is essential for uncovering the functional organization of complex networks. While traditional methods often rely on edge density, motif-based approaches use higher-order structural patterns to identify communities. However, existing research frequently employs conventional motifs, such as triangles or 4-node cliques, or lacks validation against networks with ground-truth communities. This study addresses these limitations by systematically evaluating eight small motifs across both synthetic and real-world networks with known community structures. We propose a framework that transforms unweighted graphs into weighted representations by assigning weights to node pairs based on their co-occurrence frequency within specific graphlets, while also preserving information about the original edges, rather than creating a potentially sparse (hyper)network. Thus, graphlet adjacency captures the topological complexity of a node by accounting for both its direct edges and the local connectivity patterns of its neighbors; this higher-order information is vital for accurate community detection. Our results demonstrate that graphlet-based weighting significantly enhances community detection in networks. We find that no single "universal" motif optimizes performance across all real-world networks. Contrary to the prevailing emphasis on dense, clique-based structures, our findings reveal that simple path-like motifs often yield superior performance in real-world networks. These results suggest that relying exclusively on cliques may overlook critical connectivity patterns, offering a new perspective on how higher-order structures define communities in networks.