Graph Characterization via Backtrackless Paths

Random walks on graphs have been extensively used for graph characterization. Positive kernels between labeled graphs have been proposed recently. In this paper we use backtrackless paths for gauging the similarity between graphs. We introduce efficient algorithms for characterizing both labeled and unlabeled graphs. First we show how to define efficient kernels based on backtrackless paths for labeled graphs. Second we show how the pattern vectors composed of backtrackless paths of different lengths can be use to characterize unlabeled graphs. The proposed methods are then applied to both labeled and unlabeled graphs.