Privacy-Preserving Triangle Counting in Distributed Graphs

Together with the popularity of graph structure in real world data, graph analysis has become an attractive research topic. Triangle counting is one of typical graph mining tasks and plays a significant role in complex network analysis, with a wide range of applications in social network analysis, spam detection, and computer-aided design applications. Given the sensitive nature of graph data, the disclosure of graph content for the purpose of analysis may raise a major privacy concern to both individuals and organizations. In this paper, we propose a protocol for privacy-preserving triangle counting when the overall graph is distributed to different parties. We firstly present the solution in a two-party scenario and then extend the protocol to any number of participating parties. The graph structure is represented by an adjacency matrix, and cryptographic secure matrix computation is utilized to tackle the problem. A secure multi-party power of matrix sum protocol is proposed to serve as a building block for the solution. We have evaluated the computational complexity and scalability of the proposed protocols both analytically and empirically. The results show that the protocols are efficient and scalable for small and medium size data.