The Node-Similarity Distribution of Complex Networks and Its Applications in Link Prediction (Extended Abstract)

Node-similarity distributions not only characterize different types of complex networks, but also offer insights in the structural predictability of complex networks, and even facilitate prediction tasks in complex networks. By means of the generating function, we propose a framework to calculate the common neighbor based similarity (CNS) distributions, offering theoretical results of similarity distributions of various complex networks. Furthermore, we apply node-similarity distributions to link prediction, a key task in network analysis. Specifically, by deriving analytical solutions for two metrics: i) precision and ii) area under the receiver operating characteristic curve (AUC), we give theoretical evaluation of link prediction. Also, by analyzing i) the expected prediction accuracy of similarity scores and ii) optimal prediction priority of unconnected node pairs, we optimize link prediction with similarity distributions. Simulation results confirm our findings and also validate the proposed methods for evaluating and optimizing link prediction.