Overlapping community detection in weighted networks via hierarchical clustering.

In real-world networks, community structures often appear as tightly connected clusters of nodes, with recent studies suggesting a hierarchical organization where larger groups subdivide into smaller ones across different levels. This hierarchical structure is particularly complex in trade networks, where actors typically belong to multiple communities due to diverse business relationships and contracts. To address this complexity, we present a novel algorithm for detecting hierarchical structures of overlapping communities in weighted networks, focusing on the interdependency between internal and external quality metrics for evaluating the detected communities. The proposed Graph Hierarchical Agglomerative Clustering (GHAC) approach utilizes maximal cliques as the basis units for hierarchical clustering. The algorithm measures dissimilarities between clusters using the minimal closed trail distance (CT-distance) and the size of maximal cliques within overlaps, capturing the density and connectivity of nodes. Through extensive experiments on synthetic networks with known ground truth, we demonstrate that the adjusted Silhouette index is the most reliable internal metric for determining the optimal cut in the dendrogram. Experimental results indicate that the GHAC method is competitive with widely used community detection techniques, particularly in networks with highly overlapping communities. The method effectively reveals the hierarchical structure of communities in weighted networks, as demonstrated by its application to the OECD weighted trade network, which describes the balanced trade value of bilateral trade relations.