Using a simple deterministic model for the Internet graph we show that the eigenvalue power-law distribution for its adjacency matrix is a direct consequence of the degree distribution and that the graph must contain many star subgraphs.

This paper introduces a family of modular, self-similar, small-world graphs with clustering zero. Relevant properties of this family are comparable to those of some networks associated with technological systems with a low clustering, like the power grid or some electronic circuits. Moreover,...

We propose a simple algorithm which produces a new category of networks, high-dimensional random Apollonian networks, with small-world and scale-free characteristics. We derive analytical expressions for their degree distributions and clustering coefficients which are determined by the dimension...

In this paper we study the reconstruction of a network topology from the eigenvalues of its Laplacian matrix. We introduce a simple cost function and consider the tabu search combinatorial optimization method, while comparing its performance when reconstructing different categories of...

In this paper we give an exact analytical expression for the number of spanning trees of an infinite family of outerplanar, small-world and self-similar graphs. This number is an important graph invariant related to different topological and dynamic properties of the graph, such as its...

Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases — usually associated with topological restrictions — their...