HALO: A FUZZY MEMBERSHIP FRAMEWORK FOR MULTI COMMUNITY NODE ASSIGNMENT IN NETWORKS

Leader-based community detection methods build communities around influential leader nodes rather than treating every node symmetrically. The recent algorithm TALB fuses topological similarity and node-attribute similarity into a single information matrix, but like its predecessors, commits every node to exactly one hard community, a poor fit for networks in which nodes belong to more than one social or thematic group. This study contributes new knowledge on the generalisability of fuzzy-membership overlap detection across leader-based and non-leader-based backbones and on the previously unquantified gap between synthetic and real-world overlap-detection accuracy. We propose HALO, a fuzzy-membership mechanism that reuses TALB's own information matrix, at no extra computational cost, to turn any hard partition into an overlapping one via a tunable threshold parameter tau. We test the hypothesis that HALO's benefit is attributable to the mechanism itself rather than to a specific backbone. HALO-TALB, applied directly on TALB, improves the Omega index and F1 score by up to 9 points over hard TALB on a synthetic benchmark, though a topology-only baseline remains competitive at high noise. HALO-GM, which decouples the mechanism from TALB's leader heuristic using a greedy-modularity backbone, resolves this gap, raising the Omega index from 0.79 to 0.99 and confirming that the mechanism generalizes across backbones. However, on ten real ego-Facebook networks with genuine overlapping ground truth, HALO never improves on a plain hard partition, even under oracle threshold selection; we trace this to the much richer overlap structure of real social circles and identify adapting HALO's membership rule to this regime as the key open problem. These findings support the mechanism's backbone-independence but show its practical benefit depend on overlap density, a boundary this study characterizes but does not yet resolve.