If vertices or edges of a networked dynamical system -- such as the brain -- are not accessible, a widely-used approach is to resort to the functional network ansatz. Such a network is derived from analyzing properties of interactions between system units (vertices) to draw conclusions about the organization of the structural network. Despite some progress in this active field of research, there are still problems that evade from a satisfactory solution. We investigate if and to what extent important properties of a functional network on the global and the local scale match those of the corresponding structural network. We derive functional networks from characterizing interactions in paradigmatic oscillator networks using widely-used time-series analysis techniques. Surprisingly, we observe local characteristics of key constituents of functional networks, identified with different centrality concepts, to largely coincide with the structural networks' analogues, while global topological and spectral aspects deviate.
Joint work with Thorsten Rings and Timo Bröhl
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