title: Network morphospace.
abstract: The structure of complex networks has attracted much attention in recent years. It has been noted that many real-world examples of networked systems share a set of common architectural features. This raises important questions about their origin, for example whether such network attributes reflect common design principles or constraints imposed by selectional forces that have shaped the evolution of network topology. Is it possible to place the many patterns and forms of complex networks into a common space that reveals their relations, and what are the main rules and driving forces that determine which positions in such a space are occupied by systems that have actually evolved? We suggest that these questions can be addressed by combining concepts from two currently relatively unconnected fields. One is theoretical morphology, which has conceptualized the relations between morphological traits defined by mathematical models of biological form. The second is network science, which provides numerous quantitative tools to measure and classify different patterns of local and global network architecture across disparate types of systems. Here, we explore a new theoretical concept that lies at the intersection between both fields, the 'network morphospace'. Defined by axes that represent specific network traits, each point within such a space represents a location occupied by networks that share a set of common 'morphological' characteristics related to aspects of their connectivity. Mapping a network morphospace reveals the extent to which the space is filled by existing networks, thus allowing a distinction between actual and impossible designs and highlighting the generative potential of rules and constraints that pervade the evolution of complex systems.
authors.affiliation: Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405-7007, USA.
authors.forename: Andrea
authors.initials: A
authors.lastname: Avena-Koenigsberger
authors.affiliation: Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405-7007, USA Indiana University Network Science Institute, Indiana University, Bloomington, IN 47405, USA.
authors.forename: Joaquín
authors.initials: J
authors.lastname: Goñi
authors.affiliation: ICREA-Complex Systems Laboratory, Universitat Pompeu Fabra (GRIB), Dr Aiguader 80, 08003 Barcelona, Spain Institut de Biologia Evolutiva, CSIC-UPF, Pg Maritim de la Barceloneta 37, 08003 Barcelona, Spain Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA.
authors.forename: Ricard
authors.initials: R
authors.lastname: Solé
authors.affiliation: Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405-7007, USA Indiana University Network Science Institute, Indiana University, Bloomington, IN 47405, USA osporns@indiana.edu.
authors.forename: Olaf
authors.initials: O
authors.lastname: Sporns
mesh_terms: D008962:Models, Theoretical
keywords: Pareto optimality; brain connectivity; complexity; evolution; graph theory