Toward Accurate Butterfly Counting with Edge Privacy Preserving in Bipartite Networks

Butterfly counting is widely used to analyze bipartite networks, but counting butterflies in original bipartite networks can reveal sensitive data and pose a risk of individual privacy, specifically edge privacy. Current privacy notions do not fully address the needs of both user-user and user-item bipartite networks. In this paper, we propose a novel privacy notion, edge decentralized differential privacy (edge DDP), which preserves edge privacy in any bipartite network. We also design the randomized edge protocol (REP) to perturb real edges in bipartite networks. However, a significant amount of noise in perturbed bipartite networks often leads to an overcount of butterflies. To achieve accurate butterfly counting, we design the randomized group protocol (RGP) to reduce noise. By combining REP and RGP, we propose a two-phase framework called butterfly counting in limitedly synthesized bipartite networks (BC-LimBN) to synthesize networks for accurate butterfly counting. BC-LimBN has been rigorously proven to satisfy edge DDP. Our experiments on various datasets confirm the high accuracy of BC-LimBN in butterfly counting and its superiority over competitors, with a mean relative error of less than 10% at most. Furthermore, our experiments show that BC-LimBN has a low time cost, requiring only a few seconds on our datasets.