In this talk a new measurement to compare two large-scale graphs based on the theory of quantum probability is introduced. The proposed distance between two graphs is defined as the distance between the corresponding moment of their spectral distributions. It is shown that the spectral distributions of their adjacency matrices in a vector state include information about both their eigenvalues and the corresponding eigenvectors. Moreover, we prove that the proposed distance is graph invariant and sub-structure invariant.
Computational results for real large-scale graphs show that its accuracy is better than any existing methods and time cost is extensively cheap.


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