Estimate the number of triangles in real-world graph streams

Abstract

Estimating the number of triangles in the graph streams is the basis of data mining, which aims to design an efficient graph stream algorithm to estimate the number of triangles in graph. Real-world graph is a multi-layer graph encompassing multiple distinct types of connectivity. The state-of-the-art approaches that counting triangles mainly focus on a general graph and cannot be applied for multi-layer graph, since duplicated edges across different layers exist. In this paper, we give the concept of several triads and triangles under the multilayer network, which truly reflect the real-world network topology. And we design a new two-stage sample algorithm based on reservoir sampling and triad sampling under real-world graph streams which solve the problem of more data brought by multi-layer networks. The algorithm is also a one-pass algorithm, and it can calculate the number of all types of triangles at the same time. We analyze the expectation and variance of the estimations and show that the algorithm is unbiased and stable. Our experimental results demonstrate that algorithm has good time efficiency and accuracy.