Controllability of Hypergraphs
This work addresses controllability for hypergraphs, which is a domain-specific problem in network science, and appears incremental as it extends existing controllability concepts to hypergraphs using tensor methods.
The paper tackles the problem of controllability in hypergraphs by developing a tensor-based dynamical system representation and deriving a Kalman-rank-like condition to determine the minimum number of control nodes (MCN) needed for controllability, with applications in simulated and real biological networks.
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.