Controllability of Hypergraphs
Can Chen, Amit Surana, Anthony M. Bloch, Indika Rajapakse
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.
Topics & Concepts
ControllabilityHypergraphMultilinear mapRobustness (evolution)MathematicsMeasure (data warehouse)Discrete mathematicsRobust controlPolynomialHeuristicDynamical systems theoryMathematical optimizationTensor productNetwork controllabilityControllability GramianControl systemDegree (music)Tensor (intrinsic definition)Linear dynamical systemTopology (electrical circuits)Linear systemApplied mathematicsComputer scienceControl (management)Singular valueTime complexityTheoretical computer scienceDistribution (mathematics)Dynamical system (definition)Tensor algebraDegree distributionTensor decomposition and applicationsGene Regulatory Network AnalysisDistributed Control Multi-Agent Systems