Measuring Two-Event Structural Correlations on Graphs
  Real-life graphs usually have various kinds of events happening on them, e.g., product purchases in online social networks and intrusion alerts in computer networks. The occurrences of events on the same graph could be correlated, exhibiting either attraction or repulsion. Such structural correlations can reveal important relationships between different events. Unfortunately, correlation relationships on graph structures are not well studied and cannot be captured by traditional measures. In this work, we design a novel measure for assessing two-event structural correlations on graphs. Given the occurrences of two events, we choose uniformly a sample of "reference nodes" from the vicinity of all event nodes and employ the Kendall's tau rank correlation measure to compute the average concordance of event density changes. Significance can be efficiently assessed by tau's nice property of being asymptotically normal under the null hypothesis. In order to compute the measure in large scale networks, we develop a scalable framework using different sampling strategies. The complexity of these strategies is analyzed. Experiments on real graph datasets with both synthetic and real events demonstrate that the proposed framework is not only efficacious, but also efficient and scalable. 
Ziyu Guan, Xifeng Yan, Lance M. Kaplan
cs.DB