Controllability of Hypergraphs
Optimization and Control
2021-03-25 v3 Machine Learning
Social and Information Networks
Systems and Control
Systems and Control
Abstract
In this paper, we develop a notion of controllability for hypergraphs via tensor algebra and polynomial control theory. Inspired by uniform hypergraphs, we propose a new tensor-based multilinear dynamical system representation, and derive a Kalman-rank-like condition to determine the minimum number of control nodes (MCN) needed to achieve controllability of even uniform hypergraphs. We present an efficient heuristic to obtain the MCN. MCN can be used as a measure of robustness, and we show that it is related to the hypergraph degree distribution in simulated examples. Finally, we use MCN to examine robustness in real biological networks.
Cite
@article{arxiv.2005.12244,
title = {Controllability of Hypergraphs},
author = {Can Chen and Amit Surana and Anthony Bloch and Indika Rajapakse},
journal= {arXiv preprint arXiv:2005.12244},
year = {2021}
}
Comments
12 pages, 9 figures, 1 table, IEEE Transactions on Network Science and Engineering, accepted to appear