On some general operators of hypergraphs. (English) Zbl 1512.05307
Summary: Here we introduce connectivity operators, namely, diffusion operators, general Laplacian operators, and general adjacency operators for hypergraphs. These operators are generalisations of some conventional notions of apparently different connectivity matrices associated with hypergraphs. In fact, we introduce here a unified framework for studying different variations of the connectivity operators associated with hypergraphs at the same time. Eigenvalues and corresponding eigenspaces of the general connectivity operators associated with some classes of hypergraphs are computed. Applications such as random walks on hypergraphs, dynamical networks, and disease transmission on hypergraphs are studied from the perspective of our newly introduced operators. We also derive spectral bounds for the weak connectivity number, degree of vertices, maximum cut, bipartition width, and isoperimetric constant of hypergraphs.
MSC:
| 05C65 | Hypergraphs |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 37C99 | Smooth dynamical systems: general theory |
| 39A12 | Discrete version of topics in analysis |
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 92B25 | Biological rhythms and synchronization |
Keywords:
hypergraph; eigenvalues of hypergraphs; diffusion on hypergraphs; matrices related to hypergraphsReferences:
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