Link Prediction Based on Graph Topology: The Predictive Value of Generalized Clustering Coefficient

Abstract

linkages among data objects is a fundamental data mining task in various application domains, including recommender systems, information retrieval, automatic Web hyperlink generation, record linkage, and communication surveillance. In many contexts link prediction is entirely based on the linkage information itself (a prominent example is the collaborative filtering recommendation). Link-structure based link prediction is closely related to a parallel and almost separate stream of research on topological modeling of large-scale graphs. Graph topological modeling builds on random graph theory to find parsimonious graph generation models reproducing empirical topological measures that summarize the global structure of a graph, such as clustering coefficient, average path length, and degree distribution. These well-studied topological measures and graph generation models have direct implications on link prediction. This paper represents initial efforts to explore the connection between link prediction and graph topology. The focus is exclusively on the predictive value of the clustering coefficient measure. The standard clustering coefficient measure is generalized to capture higher-order clustering tendencies. The proposed framework consists of a cycle formation link probability model, a procedure for estimating model parameters based on the generalized clustering coefficients, and model-based link prediction generation. Using the Enron email dataset we demonstrate that the proposed cycle formation model corresponded closely with the actual link probabilities and the link prediction algorithm based on this model outperformed existing algorithms.