Related papers: Discrete Scale Invariance in Scale Free Graphs
The debate on the correlation properties of galaxy structures has having an increasing interest during the last year. In this lecture we discuss the claims of different authors who have criticized our approach and results. In order to have…
The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that…
Conserved quantities are obtained and analyzed in the new models with global scale invariance recently proposed. Such models allow for non tivial scalar field potentials and masses for particles, so that the scale symmetry must be broken…
The role played by non-extensive thermodynamics in physical systems has been under intense debate for the last decades. Some possible mechanisms that could give rise to non-extensive statistics have been formulated along the last few years,…
We study the statistical properties of the generation of random graphs according the configuration model, where one assigns randomly degrees to nodes. This model is often used, e.g., for the scale-free degree distribution ~d^gamma. For the…
The turbulent dynamics of nearby and extragalactic gas structures can be studied with the column density power spectrum, which is often described by a broken power-law.In an extragalactic context, the breaks in the power spectra have been…
Hierarchical networks actually have many applications in the real world. Firstly, we propose a new class of hierarchical networks with scale-free and fractal structure, which are the networks with triangles compared to traditional…
The temporal evolution of mechanical energy and spatially-averaged crack speed are both monitored in slowly fracturing artificial rocks. Both signals display an irregular burst-like dynamics, with power-law distributed fluctuations spanning…
We discuss a category of graphs, recursive clique trees, which have small-world and scale-free properties and allow a fine tuning of the clustering and the power-law exponent of their discrete degree distribution. We determine relevant…
In this paper, we introduce the notion of an energy graph as a simple, directed and vertex labeled graph $G$ such that the arcs $(v_i, v_j) \notin A(G)$ if $i > j$ for all distinct pairs $v_i,v_j$ and at least one vertex $v_k$ exists such…
Fractal (or transfractal) features are common in real-life networks and are known to influence the dynamic processes taking place in the network itself. Here we consider a class of scale-free deterministic networks, called $(u,v)$-flowers,…
We study the statistics of the dissipated energy in the two-dimensional random fuse model for fracture under different imposed strain conditions. By means of extensive numerical simulations we compare different ways to compute the…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…
We consider a family of directed exponential random graph models parametrized by edges and outward stars. Much of the important statistical content of such models is given by the normalization constant of the models, and in particular, an…
We introduce a segmentation algorithm to probe temporal organization of heterogeneities in human heartbeat interval time series. We find that the lengths of segments with different local values of heart rates follow a power-law…
We study the dipole picture of high-energy virtual-photon-proton scattering. It is shown that different choices for the energy variable in the dipole cross section used in the literature are not related to each other by simple arguments…
The sum of the absolute values of the eigenvalues of a graph is called the energy of the graph. We study the problem of finding graphs with extremal energy within specified classes of graphs. We develop tools for treating such problems and…
Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the…
A large number of complex networks, both natural and artificial, share the presence of highly heterogeneous, scale-free degree distributions. A few mechanisms for the emergence of such patterns have been suggested, optimization not being…
Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…