Comparing large-scale graphs based on quantum probability theory

Understand

In this paper, a new measurement to compare two large-scale graphs based on the theory of quantum probability is proposed.

• An explicit form for the spectral distribution of the corresponding adjacency matrix of a graph is established.
• Our proposed distance between two graphs is defined as the distance between the corresponding moment matrices of their spectral distributions.
• It is shown that the spectral distributions of their adjacency matrices in a vector state includes information not only about their eigenvalues, but also about the corresponding eigenvectors.