The Kuramoto model for an ensemble of coupled oscillators provides a
paradigmatic example of non-equilibrium transitions between an incoherent and a
synchronized state. Here we analyze populations of almost identical oscillators
in arbitrary interaction networks. Our aim is to extract topological features
of the connectivity pattern from purely dynamical measures, based on the fact
that in a heterogeneous network the global dynamics is not only affected by the
distribution of the natural frequencies, but also by the location of the
different values. In order to perform a quantitative study we focused on a very
simple frequency distribution considering that all the frequencies are equal
but one, that of the pacemaker node. We then analyze the dynamical behavior of
the system at the transition point and slightly above it, as well as very far
from the critical point, when it is in a highly incoherent state. The gathered
topological information ranges from local features, such as the single node
connectivity, to the hierarchical structure of functional clusters, and even to
the entire adjacency matrix.Comment: 11 pages, 10 figure
