  Boltzmann-Gibbs statistical mechanics applies satisfactorily to a plethora of
systems. It fails however for complex systems generically involving strong
space-time entanglement. Its generalization based on nonadditive $q$-entropies
adequately handles a wide class of such systems. We show here that
scale-invariant networks belong to this class. We numerically study a
$d$-dimensional geographically located network with weighted links and exhibit
its 'energy' distribution per site at its quasi-stationary state. Our results
strongly suggest a correspondence between the random geometric problem and a
class of thermal problems within the generalised thermostatistics. The
Boltzmann-Gibbs exponential factor is generically substituted by its
$q$-generalisation, and is recovered in the $q=1$ limit when the nonlocal
effects fade away. The present connection should cross-fertilise experiments in
both research areas.
