Tensor entropy for uniform hypergraphs

12/20/2019 ∙ by Can Chen, et al. ∙ 24

In this paper, we develop a new notion of entropy for uniform hypergraphs, which are generalized from graphs, based on tensor theory. In particular, we employ the probability distribution of the generalized singular values, calculated from the higher-order singular value decomposition of the Laplacian tensors, to fit into the Shannon entropy formula. It is shown that this tensor entropy is an extension of von Neumann entropy for graphs. We establish results on the lower and upper bounds of the entropy and demonstrate that it is a measure of regularity, relying on the vertex degrees, path lengths, clustering coefficients and nontrivial symmetricity, for uniform hypergraphs with two simulated examples.

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