A new measure of network efficiency

We address the issue of the dynamical origin of scale-free link distributions. We study a two-dimensional lattice of cooperatively interacting units. Although the units interact only with the four nearest neighbors, a sufficiently large cooperation strength generates dynamically a scale-free network with the power law index ν approaching 1. We explain this result by using a new definition of network efficiency determined by the Euclidean distance between correlated units. According to this definition the link distribution favoring long-range connections makes efficiency increase. We embed an ad hoc scale-free network with power index ν ≥ 1 into a Euclidean two-dimensional space and show that the network efficiency becomes maximal as ν approaches 1. We therefore conclude that ν = 1 emerging from the cooperative interaction of units may be a consequence of the principle of network maximal efficiency.