The structural properties and the spanning trees entropy of the generalized Fractal Scale-Free Lattice

Abstract

Abstract Enumerating all the spanning trees of a complex network is theoretical defiance for mathematicians, electrical engineers and computer scientists. In this article, we propose a generalization of the Fractal Scale-Free Lattice and we study its structural properties. As its degree distribution follows a power law, we prove that the proposed generalization does not affect the scale-free property. In addition, we use the electrically equivalent transformations to count the number of spanning trees in the generalized Fractal Scale-Free Lattice. Finally, in order to evaluate the robustness of the generalized lattice, we compute and compare its entropy with other complex networks having the same average degree.