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MomentSA: A Fast and Accurate Method for Stochastic Kronecker Graph Parameter Computing

Stochastic Kronecker Graph model is widely used to generate synthetic graphs that simulate real-world graphs. In this model, the initiator matrix decides the degree to which the synthetic graph approximates the real-world graph. The computing of initiator matrix, however, requires that the number of the nodes of input graph is the power of the dimension of the initiator matrix. In order to fulfill such requirement, some methods (e.g., KronFit and Moment) add isolated nodes to the input graph, which damages the input graph's properties. Other method (e.g., KronEM) predicts the links between the nodes after adding isolated nodes. Unfortunately, the prediction dramatically increases the complexity of computing. In this paper, we propose a method named as MomentSA to solve the problems. Our method completes the input graphs by leveraging the law of property changes of graphs, which does not need to predict the links as method KronEM. Simultaneously, our method uses the moment-based estimation and ADAM (Adaptive Moment Estimation) method to compute the initiator matrix, which can compute the initiator matrix quickly. Experiment results on our prototype implementation suggest that the initiator matrix computed from our method is more accurate than existing state-of-art systems, and the speed of computing is about three to four orders of magnitude faster than state-of-art systems.