title: Network susceptibilities: Theory and applications.
abstract: We introduce the concept of network susceptibilities quantifying the response of the collective dynamics of a network to small parameter changes. We distinguish two types of susceptibilities: vertex susceptibilities and edge susceptibilities, measuring the responses due to changes in the properties of units and their interactions, respectively. We derive explicit forms of network susceptibilities for oscillator networks close to steady states and offer example applications for Kuramoto-type phase-oscillator models, power grid models, and generic flow models. Focusing on the role of the network topology implies that these ideas can be easily generalized to other types of networks, in particular those characterizing flow, transport, or spreading phenomena. The concept of network susceptibilities is broadly applicable and may straightforwardly be transferred to all settings where networks responses of the collective dynamics to topological changes are essential.
authors.affiliation: Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany.
authors.forename: Debsankha
authors.initials: D
authors.lastname: Manik
authors.affiliation: Department of Physics and Earth Sciences, Jacobs University, 28759 Bremen, Germany.
authors.forename: Martin
authors.initials: M
authors.lastname: Rohden
authors.affiliation: Physics of Biological Organization, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany.|Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
authors.forename: Henrik
authors.initials: H
authors.lastname: Ronellenfitsch
authors.affiliation: Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany.
authors.forename: Xiaozhu
authors.initials: X
authors.lastname: Zhang
authors.affiliation: Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany.|Fakultät Technik und Informatik, Hochschule für Angewandte Wissenschaften Hamburg, 20099 Hamburg, Germany.
authors.forename: Sarah
authors.initials: S
authors.lastname: Hallerberg
authors.affiliation: Forschungszentrum Jülich, Institute for Energy and Climate Research-Systems Analysis and Technology Evaluation (IEK-STE), 52428 Jülich, Germany.|Institute for Theoretical Physics, University of Cologne, 50937 Köln, Germany.
authors.forename: Dirk
authors.initials: D
authors.lastname: Witthaut
authors.affiliation: Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany.|Faculty of Physics, Georg August University Göttingen, 37073 Göttingen, Germany.|Department of Physics, University of Darmstadt, 64289 Darmstadt, Germany.
authors.forename: Marc
authors.initials: M
authors.lastname: Timme