vix.ing · top · new · best · stats · spec

Controllability of Hypergraphs

2020/05/31 by Can Chen, Amit Surana, Anthony Bloch +1 · 1 citation
Mathematics · Computer Science · Engineering · #math.OC #cs.LG #cs.SI #cs.SY #eess.SY

paper · pdf · doi:10.1109/tnse.2021.3068203

12 pages, 9 figures, 1 table, IEEE Transactions on Network Science and Engineering, accepted to appear

arxiv created 2021/03/20 · arxiv updated 2021/03/25

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.

Cited by