相关论文: Evolving Scale-Free Network Model with Tunable Clu…
Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model…
In this note we make some specific observations on the distribution of the degree of a given vertex in certain model of randomly growing networks. The rule for network growth is the following. Starting with an initial graph of minimum…
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…
Many networks generated by nature have two generic properties: they are formed in the process of {preferential attachment} and they are scale-free. Considering these features, by interfering with mechanism of the {preferential attachment},…
We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation…
Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections, and rewiring of existing links, we study {\em ad hoc} networks, where one also has to contend with rapid and…
Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…
We study an evolving spatial network in which sequentially arriving vertices are joined to existing vertices at random according to a rule that combines preference according to degree with preference according to spatial proximity. We…
We are interested in the probability that two randomly selected neighbors of a random vertex of degree (at least) $k$ are adjacent. We evaluate this probability for a power law random intersection graph, where each vertex is prescribed a…
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…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability to get connected to a site at…
In this contribution we introduce local attachment as an universal network-joining protocol for peer-to-peer networks, social networks, or other kinds of networks. Based on this protocol nodes in a finite-size network dynamically create…
Many real systems possess accelerating statistics where the total number of edges grows faster than the network size. In this paper, we propose a simple weighted network model with accelerating growth. We derive analytical expressions for…
Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the…
A network growth mechanism based on a two-step preferential rule is investigated as a model of network growth in which no global knowledge of the network is required. In the first filtering step a subset of fixed size $m$ of existing nodes…
The availability of large scale streaming network data has reinforced the ubiquity of power-law distributions in observations and enabled precision measurements of the distribution parameters. The increased accuracy of these measurements…
We study the growth of a reference network with aging of sites defined in the following way. Each new site of the network is connected to some old site with probability proportional (i) to the connectivity of the old site as in the…
This paper presents a tighter bound on the degree distribution of arbitrary P\'{o}lya urn graph processes, proving that the proportion of vertices with degree $d$ obeys a power-law distribution $P(d) \propto d^{-\gamma}$ for $d \leq…
We develop a simple theoretical framework for the evolution of weighted networks that is consistent with a number of stylized features of real-world data. In our framework, the Barabasi-Albert model of network evolution is extended by…