Tensor Entropy for Uniform Hypergraphs
arXiv:1912.09624 · doi:10.1109/TNSE.2020.3002963
Abstract
In this paper, we develop the notion of entropy for uniform hypergraphs via tensor theory. 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. We show that this tensor entropy is an extension of von Neumann entropy for graphs. In addition, we establish results on the lower and upper bounds of the entropy and demonstrate that it is a measure of regularity for uniform hypergraphs in simulated and experimental data. We exploit the tensor train decomposition in computing the proposed tensor entropy efficiently. Finally, we introduce the notion of robustness for uniform hypergraphs.
12 pages, 11 figures, 1 table, IEEE Transactions on Network Science and Engineering, accepted to appear
References in corpus (8)
- Classes of behavior of small-world networks
- High-resolution measurements of face-to-face contact patterns in a primary school
- Time varying networks and the weakness of strong ties
- Mitigation of infectious disease at school: targeted class closure vs school closure
- Tensor-based dynamic mode decomposition
- Searching for Representative Modes on Hypergraphs for Robust Geometric Model Fitting
- Some families of density matrices for which separability is easily tested
- Measures of Correlation for Multiple Variables