Measuring distance or some other form of proximity between objects is a standard data mining tool. Connection subgraphs were recently proposed as a way to demonstrate proximity between nodes in networks. We propose a new way of measuring and extracting proximity in networks called "cycle free effective conductance" (CFEC). Our proximity measure can handle more than two endpoints, directed edges, is statistically well-behaved, and produces an effectiveness score for the computed subgraphs. We provide an efficient algorithm. Also, we report experimental results and show examples for three large network data sets: a telecommunications calling graph, the IMDB actors graph, and an academic co-authorship network. Categories and Subject Descriptors H.2.8 [Database Management]: Database Applications--Data Mining; G.2.2 [Discrete Mathematics]: Graph Theory--Graph Algorithms General Terms Algorithms, Human Factors Keywords proximity, random walks, escape probability, cycle-free escape...
Yehuda Koren, Stephen C. North, Chris Volinsky