  Based on a local greedy numerical algorithm, we compute the topology of
weighted, directed, and of unlimited extension networks of non identical
Kuramoto oscillators which simultaneously satisfy 2 criteria: i) global
frequency synchronisation and ii) minimal total mass of the connection weights.
This problem has been the subject of many previous interesting studies, but
from our best knowledge, this is the first time that no a priori constraint is
imposed, either on the form or on the dynamics of the connections. The results
are surprising: the optimal networks turn out to be strongly symmetric, very
economical, to display a strong rich club structure, and next to the already
reported strong correlation between natural frequencies and the weight of
incoming connections, we also observe a correlation, even more marked, between
these same natural frequencies and the weight of outgoing connections. The
latter result is at odds with theoretical predictions.

Adaptation and Self-Organizing Systems