Controllability of Uniform Hypergraphs.
Year: 2020
Type: preprint
Abstract: In this paper, we develop the notion of controllability for uniform hypergraphs via tensor algebra and the theory of polynomial control. We propose a tensor-based multilinear system representation to characterize the multidimensional state dynamics of uniform hypergraphs, and derive a Kalman-rank-like condition to identify the minimum number of driver vertices in order to achieve full control of the whole hypergraph. We discover that the minimum number of driver vertices can be determined by the hypergraph degree distributions, and high degree vertices are preferred to be the drivers in the chain, ring and star hypergraph configurations. Finally, we present some preliminary stability results for the corresponding discrete multilinear systems.
Source: arXiv (Cornell University)
Authors: Can Chen, Anthony M. Bloch, Indika Rajapakse
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3026863560