The relationship between network structure and dynamics is one of the most extensively investigated problems in the theory of complex systems of recent years. Understanding this relationship is of relevance to a range of disciplines-from neuroscience to geomorphology. A major strategy of investigating this relationship is the quantitative comparison of a representation of network architecture (structural connectivity, SC) with a (network) representation of the dynamics (functional connectivity, FC). Here, we show that one can distinguish two classes of functional connectivity-one based on simultaneous activity (co-activity) of nodes, the other based on sequential activity of nodes. We delineate these two classes in different categories of dynamical processes-excitations, regular and chaotic oscillators-and provide examples for SC/FC correlations of both classes in each of these models. We expand the theoretical view of the SC/FC relationships, with conceptual instances of the SC and the two classes of FC for various application scenarios in geomorphology, ecology, systems biology, neuroscience and socio-ecological systems. Seeing the organisation of dynamical processes in a network either as governed by co-activity or by sequential activity allows us to bring some order in the myriad of observations relating structure and function of complex networks.

Advancing Systems Analysis Program International Institute for Applied Systems Analysis Laxenburg 2361 Austria

Aix Marseille Université CNRS Institut de Neurosciences de la Timone Marseille France

Aix Marseille Université Inserm Institut de Neurosciences des Systèmes Marseille France

Department of Biological Sciences Towson University Towson Maryland 21252 USA

Department of Computational Neuroscience University Medical Center Eppendorf Hamburg University Germany

Department of Cultural Geography University of Groningen 9747 AD Groningen The Netherlands

Department of Environmental Studies Masaryk University 60200 Brno Czech Republic

Department of Geography and Regional Research University of Vienna Universitätsstr 7 1010 Vienna Austria

Department of Geography Durham University Durham DH1 3LE UK

Department of Life Sciences and Chemistry Jacobs University Bremen 28759 Bremen Germany

Department of Sustainability Governance and Methods Modul University Vienna 1190 Vienna Austria

Institute of Hydrobiology and Aquatic Ecosystem Management 1180 Vienna Austria

Regional Science and Environmental Research Institute for Advanced Studies 1080 Vienna Austria

University of Strasbourg Institute for Advanced Studies Strasbourg 67083 France

WasserCluster Lunz Biologische Station GmbH Dr Carl Kupelwieser Promenade 5 3293 Lunz am See Austria

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