Controllability and maximum matchings of complex networks

Abstract

Previously, the controllability problem of a linear time-invariant dynamical system was mapped to the maximum matching (MM) problem on the bipartite representation of the underlying directed graph, and the sizes of MMs on random bipartite graphs were calculated analytically with the cavity method at zero temperature limit. Here we present an alternative theory to estimate MM sizes based on the core percolation theory and the perfect matching of cores. Our theory is much more simplified and easily interpreted, and can estimate MM sizes on random graphs with or without symmetry between out- and in-degree distributions. Our result helps to illuminate the fundamental connection between the controllability problem and the underlying structure of complex systems.

12 pages, 3 figures, and 1 table

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Cited by in corpus (4)

• Energy cost study for controlling complex social networks with conformity behavior
• Statistical mechanics of bipartite $z$-matchings
• The network asymmetry caused by the degree correlation and its effect on the bimodality in control
• A local algorithm and its percolation analysis of bipartite $z$-matching problem