相关论文: Scale-Free Networks beyond Power-Law Degree Distri…

The "power of choice" has been shown to radically alter the behavior of a number of randomized algorithms. Here we explore the effects of choice on models of tree and network growth. In our models each new node has k randomly chosen…

How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…

This paper establishes a relation between scale-free networks and Markov chains, and proposes a computation framework for degree distributions of scale-free networks. We first find that, under the BA model, the degree evolution of…

Heavy-tailed networks are often characterized in the literature by their degree distribution's similarity to a power law. However, many heavy-tailed networks in real life do not have power-law degree distributions, and in many applications…

A spatial scale-free network is introduced and studied whose motivation has been originated in the growing Internet as well as the Airport networks. We argue that in these real-world networks a new node necessarily selects one of its…

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…

We study transport properties such as electrical and frictionless flow conductance on scale-free and Erdos-Renyi networks. We consider the conductance G between two arbitrarily chosen nodes where each link has the same unit resistance. Our…

One explanation for the impressive recent boom in network theory might be that it provides a promising tool for an understanding of complex systems. Network theory is mainly focusing on discrete large-scale topological structures rather…

Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…

A large computer program is typically divided into many hundreds or even thousands of smaller units, whose logical connections define a network in a natural way. This network reflects the internal structure of the program, and defines the…

The scale-free (SF) structure that commonly appears in many complex networks is one of the hot topics related to social, biological, and information sciences. The self-organized generation mechanisms are expected to be useful for efficient…

Several kinds of walks on complex networks are currently used to analyze search and navigation in different systems. Many analytical and computational results are known for random walks on such networks. Self-avoiding walks (SAWs) are…

We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…

We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…

The study of complex networks sheds light on the relation between the structure and function of complex systems. One remarkable result is the absence of an epidemic threshold in infinite-size scale-free networks, which implies that any…

We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all…

In this paper we provide numerical evidence of the richer behavior of the connectivity degrees in heterogeneous preferential attachment networks in comparison to their homogeneous counterparts. We analyze the degree distribution in the…

We define gradient networks as directed graphs formed by local gradients of a scalar field distributed on the nodes of a substrate network G. We derive an exact expression for the in-degree distribution of the gradient network when the…

It has been shown that many networks associated with complex systems are small-world (they have both a large local clustering coefficient and a small diameter) and they are also scale-free (the degrees are distributed according to a power…

In this study, we employ a superstatistical approach to construct q exponential and q Maxwell Boltzmann complex networks, generalizing the concept of scale free networks. By adjusting the crossover parameter {\lambda}, we control the degree…