WIGM: Discovery of Subgraph Patterns in a Large Weighted Graph

Many research areas have begun representing massive data sets as very large graphs. Thus, graph mining has been an active research area in recent years. Most of the graph mining research focuses on mining unweighted graphs. However, weighted graphs are actually more common. The weight on an edge may represent the likelihood or logarithmic transformation of likelihood of the existence of the edge or the strength of an edge, which is common in many biological networks. In this paper, a weighted subgraph pattern model is proposed to capture the importance of a subgraph pattern and our aim is to find these patterns in a large weighted graph. Two related problems are studied in this paper: (1) discovering all patterns with respect to a given minimum weight threshold and (2) finding k patterns with the highest weights. The weighted subgraph patterns do not possess the anti-monotonic property and in turn, most of existing subgraph mining methods could not be directly applied. Fortunately, the 1-extension property is identified so that a bounded search can be achieved. A novel weighted graph mining algorithm, namely WIGM, is devised based on the 1-extension property. Last but not least, real and synthetic data sets are used to show the effectiveness and efficiency of our proposed models and algorithms.