相关论文: Evolving Networks and Birth-and-Death Processes

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…

Inspired by empirical data on real world complex networks, the last few years have seen an explosion in proposed generative models to understand and explain observed properties of real world networks, including power law degree distribution…

A network is formed using the $N$ sites of an one-dimensional lattice in the shape of a ring as nodes and each node with the initial degree $k_{in}=2$. $N$ links are then introduced to this network, each link starts from a distinct node,…

What is the underlying mechanism leading to power-law degree distributions of many natural and artificial networks is still at issue. We consider that scale-free networks emerges from self-organizing process, and such a evolving model is…

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 paper, we abstract a kind of stochastic processes from evolving processes of growing networks, this process is called growing network Markov chains. Thus the existence and the formulas of degree distribution are transformed to the…

We find that a wide class of developing and decaying networks has scaling properties similar to those that were recently observed by Barab\'{a}si and Albert in the particular case of growing networks. The networks considered here evolve…

We study network growth from a fixed set of initially isolated nodes placed at random on the surface of a sphere. The growth mechanism we use adds edges to the network depending on strictly local gain and cost criteria. Only nodes that are…

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…

A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree $k$ follows a power law, decaying like $k^{-\alpha}$, often with $2 < \alpha < 3$. However,…

Understanding design principles of complex cellular organization is one of the major challenges in biology. Recent analysis of the large-scale cellular organization has revealed the scale-free nature and robustness of metabolic and protein…

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…

Barab\'asi-Albert's `Scale Free' model is the starting point for much of the accepted theory of the evolution of real world communication networks. Careful comparison of the theory with a wide range of real world networks, however,…

We study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks. In networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold…

Conventional studies of network growth models mainly look at the steady state degree distribution of the graph. Often long time behavior is considered, hence the initial condition is ignored. In this contribution, the time evolution of the…

Many real-world networks display a natural bipartite structure. Investigating it based on the original structure is helpful to get deep understanding about the networks. In this paper, some real-world bipartite networks are collected and…

We investigate a model of evolving random network, introduced by us previously {[}{\it Phys. Rev. Lett.} {\bf 83}, 5587 (1999){]} . The model is a generalization of the Bak-Sneppen model of biological evolution, with the modification that…

With the evolution of social networks, the network structure shows dynamic nature in which nodes and edges appear as well as disappear for various reasons. The role of a node in the network is presented as the number of interactions it has…

In this paper, we explore the consequences of a distinction between `live' and `dead' network nodes; `live' nodes are able to acquire new links whereas `dead' nodes are static. We develop an analytically soluble growing network model…

In spite of its relevance to the origin of complex networks, the interplay between form and function and its role during network formation remains largely unexplored. While recent studies introduce dynamics by considering rewiring processes…