Related papers: From Scale-free to Erdos-Renyi Networks

Uncorrelated random scale-free networks are useful null models to check the accuracy an the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable to generate random uncorrelated…

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…

The scale free structure p(k)~k^{-gamma} of protein-protein interaction networks can be reproduced by a static physical model in simulation. We inspect the model theoretically, and find the key reason for the model to generate apparent…

Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment…

Understanding the resilience of infrastructures such as transportation network has significant importance for our daily life. Recently, a homogeneous spatial network model was developed for studying spatial embedded networks with…

We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension…

It has recently been discovered that many biological systems, when represented as graphs, exhibit a scale-free topology. One such system is the set of structural relationships among protein domains. The scale-free nature of this and other…

In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…

In this paper, we address the logarithmic corrections to the leading power laws that govern thermodynamic quantities as a second-order phase transition point is approached. For phase transitions of spin systems on d-dimensional lattices,…

With a simple attack and repair evolution model, we investigate the stability and structural changes of the Erdos-Renyi random graphs (RG) and Barabasi-Albert scale-free (SF) networks. We introduce a new quantity, invulnerability I(s), to…

While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…

The emergence of explosive collective phenomena has recently attracted much attention due to the discovery of an explosive percolation transition in complex networks. In this Letter, we demonstrate how an explosive transition shows up in…

In this paper, we study the robustness of network topologies. We use the concept of percolation as measuring tool to assess the reliability polynomial of those systems which can be modeled as a general inhomogeneous random graph as well as…

We study the performance of Weibull and scale free Internet-like networks and compare them to a classical random graph based network. The scaling of the traffic load with the nodal degree is established, and confimed in a numerical…

In this paper, a network-based stochastic information propagation model is developed. The information flow is modeled by a probabilistic differential equation system. The numerical solution of these equations leads to the expected number of…

We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial…

Extending previous results in the literature, random colored substitution networks and degree dimension are defined in this paper. The scale-freeness of these networks is proved by introducing a new definition for degree dimension that is…

Recently the problem of classes of vulnerable vertices (represented by colors) in complex networks has been discussed, where all vertices with the same vulnerability are prone to fail together. Utilizing redundant paths each avoiding one…

Very often, when studying topological or dynamical properties of random scale-free networks, it is tacitly assumed that degree-degree correlations are not present. However, simple constraints, such as the absence of multiple edges and…

We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical…