On January 28, 2022, CSH researcher Nicola Cinardi will present his current projects via Zoom.
If you would like to join the presentation, please send an email to firstname.lastname@example.org.
Title: A generalized model for asymptotically-scale-free geographical networks
We consider a generalised d-dimensional model for asymptotically-scale-free geographical networks. Central to many networks of this kind, when considering their growth in time, is the attachment rule, i.e. the probability that a new node is attached to one (or more) preexistent nodes. In order to be more realistic, a fitness parameter η_i for each node i of the network is also taken into account to reflect the ability of the nodes to attract new ones.
Our d-dimensional model takes into account the geographical distances between nodes, with different probability distribution for η which sensibly modifies the growth dynamics. The preferential attachment rule is assumed to be Π_i∝k_i*η_i*r^(−α_A) where k_i is the connectivity of the i–th pre-existing site and α_A characterizes the importance of the euclidean distance r for the network growth. For special values of the parameters, this model recovers respectively the Bianconi–Barabási and the Barabási–Albert ones.
The present generalised model is asymptotically scale-free in all cases, and its degree distribution is very well fitted with q-exponential distributions, which optimizes the nonadditive entropy Sq, given by p(k)∝e^(−k/κ)_q≡1/[1+(q−1)k/κ]^(1/(q−1)), with (q,κ) depending uniquely only on the ratio α_A/d and the fitness distribution. Hence this model constitutes a realization of asymptotically-scale-free geographical networks within nonextensive statistical mechanics, where k plays the role of energy and κ plays the role of temperature. General scaling laws are also found for q as a function of the parameters of the model.