Fast Computing von Neumann Entropy for Large-scale Graphs via Quadratic Approximations

11/12/2018

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by   Hayoung Choi, et al.

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The von Neumann graph entropy (VNGE) can be used as a measure of graph complexity, which can be the measure of information divergence and distance between graphs. Since computing VNGE is required to find all eigenvalues, it is computationally demanding for a large-scale graph. We propose novel quadratic approximations for computing the von Neumann graph entropy. Modified Taylor and Radial projection approximations are proposed. Our methods reduce the cubic complexity of VNGE to linear complexity. Computational simulations on random graph models and various real network datasets demonstrate the superior performance.