title: Phase transitions in Pareto optimal complex networks.
abstract: The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their topological structure can be diverse, resulting from different mechanisms including multiplicative processes and optimization. In spatial networks or in graphs where cost constraints are at work, as it occurs in a plethora of situations from power grids to the wiring of neurons in the brain, optimization plays an important part in shaping their organization. In this paper we study network designs resulting from a Pareto optimization process, where different simultaneous constraints are the targets of selection. We analyze three variations on a problem, finding phase transitions of different kinds. Distinct phases are associated with different arrangements of the connections, but the need of drastic topological changes does not determine the presence or the nature of the phase transitions encountered. Instead, the functions under optimization do play a determinant role. This reinforces the view that phase transitions do not arise from intrinsic properties of a system alone, but from the interplay of that system with its external constraints.
authors.affiliation: ICREA-Complex Systems Lab, Universitat Pompeu Fabra-PRBB, Dr. Aiguader 88, 08003 Barcelona, Spain.|Institut de Biologia Evolutiva, UPF-CSIC, Passg Barceloneta, 08003 Barcelona, Spain.
authors.forename: Luís F
authors.initials: LF
authors.lastname: Seoane
authors.affiliation: ICREA-Complex Systems Lab, Universitat Pompeu Fabra-PRBB, Dr. Aiguader 88, 08003 Barcelona, Spain.|Institut de Biologia Evolutiva, UPF-CSIC, Passg Barceloneta, 08003 Barcelona, Spain.|Santa Fe Institute, 1399 Hyde Park Road, New Mexico 87501, USA.
authors.forename: Ricard
authors.initials: R
authors.lastname: Solé
mesh_terms: D008962:Models, Theoretical