Measuring Large-Scale Dynamic Graph Similarity by RICom: RWR with Intergraph Compression

Abstract

By how much is a large-scale graph transformed over time or by a significant event?' or 'how structurally similar are two large-scale graphs?' are the two questions that this paper attempts to address. The proposed method efficiently calculates and accurately produces graph similarity. Our approach is based on the well-known random walk with restart (RWR) algorithm, which quantifies relevance between nodes to express the structural and connection characteristics of graphs. Intergraph compression, which is inspired by interframe compression, merges two input graphs and reorders their nodes contributing to improved process-data storage efficiency and processing convenience. This is a boon to the RWR algorithm for large-scale graphs. The representation of a graph transformed via intergraph compression can be used to accurately show similarity because sub-matrix blocks are reordered to concentrate nonzero elements. In performing the RWR algorithm, which quantifies inter-node relevance, transformed representation of graph with Intergraph compression is efficient in space requirement and produces results more quickly and accurately over conventional graph transformation schemes. We demonstrate the validity of our method through experiments and apply it to the usage data of public transportation SmartCard in a large metropolitan area to suggest usefulness of the proposed algorithm.