  The relationship of network structure and dynamics is one of most extensively
investigated problems in the theory of complex systems of the last 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) with a (network) representation of the
dynamics (functional connectivity). Analysing such SC/FC relationships has over
the past years contributed substantially to our understanding of the functional
role of network properties, such as modularity, hierarchical organization, hubs
and cycles.
  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, Freshwater Ecology, Systems
Biology, Neuroscience and Social-Ecological Systems.
  Seeing the organization of a 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.
