We use the configuration model to generate networks having a degree
distribution that follows a q-exponential,
Pq(k)=(2−q)λ[1−(1−q)λk]1/(q−1), for arbitrary values of the
parameters q and λ. We study the assortativity and the shortest path
of these networks finding that the more the distribution resembles a pure power
law, the less well connected are the corresponding nodes. In fact, the average
degree of a nearest neighbor grows monotonically with λ−1. Moreover,
our results show that q-exponential networks are more robust against random
failures and against malicious attacks than standard scale-free networks.
Indeed, the critical fraction of removed nodes grows logarithmically with
λ−1 for malicious attacks. An analysis of the ks-core
decomposition shows that q-exponential networks have a highest ks-core,
that is bigger and has a larger ks than pure scale-free networks. Being at
the same time well connected and robust, networks with q-exponential degree
distribution exhibit scale-free and small-world properties, making them a
particularly suitable model for application in several systems.Comment: 6 pages, 8 figure