Related papers: Mean-field theory for scale-free random networks
Scale-free (SF) networks and small world networks have been found to occur in very diverse contexts. It is this striking universality which makes one look for widely applicable mechanisms which lead to the formation of such networks. In…
We present a novel type of weighted scale-free network model, in which the weight grows independently of the attachment of new nodes. The evolution of this network is thus determined not only by the preferential attachment of new nodes to…
We propose a method of generating different scale-free networks, which has several input parameters in order to adjust the structure, so that they can serve as a basis for computer simulation of real-world phenomena. The topological…
Contrary to many recent models of growing networks, we present a model with fixed number of nodes and links, where it is introduced a dynamics favoring the formation of links between nodes with degree of connectivity as different as…
The properties of scale-free random trees are investigated using both preconditioning on non-extinction and fixed size averages, in order to study the thermodynamic limit. The scaling form of volume probability is found, the connectivity…
Many real networks such as the World Wide Web, financial, biological, citation and social networks have a power-law degree distribution. Networks with this feature are also called scale-free. Several models for producing scale-free networks…
Recently, one paper in Nature(Papadopoulos, 2012) raised an old debate on the origin of the scale-free property of complex networks, which focuses on whether the scale-free property origins from the optimization or not. Because the…
We present a family of scale-free network model consisting of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and numerically. The obtained analytical solutions show that the…
Understanding the emergent macroscopic behavior of dynamical systems on networks is a crucial but challenging task. One of the simplest and most effective methods to construct a reduced macroscopic model is given by mean-field theory. The…
In contrast to the conventional wisdom that scale-free networks are prone to epidemic propagation, in the paper we present that disease spreading is inhibited in fractal scale-free networks. We first propose a novel network model and show…
We study spatial networks constructed by randomly placing nodes on a manifold and joining two nodes with an edge whenever their distance is less than a certain cutoff. We derive the general expression for the connectivity distribution of…
We present empirical evidence that land values are scale-free and introduce a network model that reproduces the observations. The network approach to urban modelling is based on the assumption that the market dynamics that generates land…
The paper is concerned with the interplay between network structure and traffic dynamics in a communications network, from the viewpoint of end-to-end performance of packet transfer. We use a model of network generation that allows the…
Recently it has been shown that a large variety of different networks have power-law (scale-free) distributions of connectivities. We investigate the robustness of such a distribution in discrete threshold networks under neutral evolution.…
Scale-free networks are prevalently observed in a great variety of complex systems, which triggers various researches relevant to networked models of such type. In this work, we propose a family of growth tree networks $\mathcal{T}_{t}$,…
We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions in real-world networks. We first provide a rigorous definition of power-law distributions, equivalent to the definition of regularly varying…
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…
Random graphs with power-law degrees can model scale-free networks as sparse topologies with strong degree heterogeneity. Mathematical analysis of such random graphs proved successful in explaining scale-free network properties such as…
Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean field predictions for the spectra of small-world models that…
The Internet, as well as many other networks, has a very complex connectivity recently modeled by the class of scale-free networks. This feature, which appears to be very efficient for a communications network, favors at the same time the…