  We introduce the concept of network susceptibilities quantifying the response
of the collective dy- namics 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 susceptibil- ities is broadly applicable and may
straightforwardly be transferred to all settings where networks responses of
the collective dynamics to topological changes are essential.
