CSH Webtalk by Nicola Cinardi: “A generalized model for asymptotically-scale-free geographical networks”

Jan 28, 2022 | 15:0016:00

Loading Events
  • This event has passed.

Event Navigation

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 office@csh.ac.at.


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 ith 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.


Jan 28, 2022