The von Neumann entropy of random multipartite graphs

Let G be a graph with n vertices and L(G) its Laplacian matrix. Define ρG=1dGL(G) to be the density matrix of G, where dG denotes the sum of degrees of all vertices of G. Let λ1,λ2,…,λn be the eigenvalues of ρG. The von Neumann entropy of G is defined as S(G)=−∑i=1nλilog2λi. In this paper, we establish a lower bound and an upper bound to the von Neumann entropy for random multipartite graphs.