title: Topological constraints on network control profiles.
abstract: Network models are designed to capture properties of empirical networks and thereby provide insight into the processes that underlie the formation of complex systems. As new information concerning network structure becomes available, it becomes possible to design models that more fully capture the properties of empirical networks. A recent advance in our understanding of network structure is the control profile, which summarizes the structural controllability of a network in terms of source nodes, external dilations, and internal dilations. Here, we consider the topological properties-and their formation mechanisms-that constrain the control profile. We consider five representative empirical categories of internal-dilation dominated networks, and show that the number of source and sink nodes, the form of the in- and out-degree distributions, and local complexity (e.g., cycles) shape the control profile. We evaluate network models that are sufficient to produce realistic control profiles, and conclude that holistic network models should similarly consider these properties.
authors.affiliation: Department of Physics, Pennsylvania State University, 104 Davey Laboratory, University Park, PA 16802.|Department of Biology, Pennsylvania State University, 208 Mueller Laboratory, University Park, PA 16802.|Department of Physics, Washington College, 300 Washington Avenue, Chestertown, MD 21620.
authors.forename: Colin
authors.initials: C
authors.lastname: Campbell
authors.affiliation: Engineering Systems and Design, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372.
authors.forename: Justin
authors.initials: J
authors.lastname: Ruths
authors.affiliation: Department of Computer Science, McGill University, McConnell Engineering Bldg. Room 318, 3480 University, Montreal, Qc, H3A 0E9, Canada.
authors.forename: Derek
authors.initials: D
authors.lastname: Ruths
authors.affiliation: Department of Biology, Pennsylvania State University, 208 Mueller Laboratory, University Park, PA 16802.
authors.forename: Katriona
authors.initials: K
authors.lastname: Shea
authors.affiliation: Department of Physics, Pennsylvania State University, 104 Davey Laboratory, University Park, PA 16802.|Department of Biology, Pennsylvania State University, 208 Mueller Laboratory, University Park, PA 16802.
authors.forename: Réka
authors.initials: R
authors.lastname: Albert