  We have obtained the Tsallis distribution from the maximum entropy approach
using constraints on the first and the second moment, together with the
normalization condition. We have constructed railway and highway communication
networks for the Moscow region and the airline network for the Russian
Federation. The fitting shows that the degree distributions for these networks
are described with the q-exponential function. In case of the railway and
highway networks, the nodes degrees distributions are well fitted with the
skewed normal distribution, while in case of the airline networks we have used
the power law distribution for fitting. The studies of the epidemics spreading
processes in these networks show that the epidemics threshold decreases with a
decrease of the constraint on the degree.
