Related papers: Degree Distributions of Growing Networks
We present exact results for the degree distribution in a directed network model that grows by node duplication (ND). Such models are useful in the study of the structure and growth dynamics of gene regulatory networks and scientific…
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…
Many natural, physical and social networks commonly exhibit power-law degree distributions. In this paper, we discover previously unreported asymmetrical patterns in the degree distributions of incoming and outgoing links in the…
The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…
We introduce a growing network model in which a new node attaches to a randomly-selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultra-small network where the average node degree grows…
The effects of link rewiring are considered for the class of directed networks where each node has the same fixed out-degree. We model a network generated by three mechanisms that are present in various networked systems; growth, global…
Network growth is currently explained through mechanisms that rely on node prestige measures, such as degree or fitness. In many real networks those who create and connect nodes do not know the prestige values of existing nodes, but only…
The analysis in this paper helps to explain the formation of growing networks with degree distributions that follow extended exponential or power-law tails. We present a generic model in which edge dynamics are driven by a continuous…
A model for directed networks is proposed and power laws for their in-degree and/or out-degree distributions are derived from the model. It is based on the Barabasi-Albert model and contains two parameters. The parameters serve as…
We compute the stationary in-degree probability, $P_{in}(k)$, for a growing network model with directed edges and arbitrary out-degree probability. In particular, under preferential linking, we find that if the nodes have a light tail…
A model for growing information networks is introduced where nodes receive new links through j-redirection, i.e. the probability for a node to receive a link depends on the number of paths of length j arriving at this node. In detail, when…
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…
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…
Network growth as described by the Duplication-Divergence model proposes a simple general idea for the evolution dynamics of natural networks. In particular it is an alternative to the well known Barab\'asi-Albert model when applied to…
We introduce and solve a model which considers two coupled networks growing simultaneously. The dynamics of the networks is governed by the new arrival of network elements (nodes) making preferential attachments to pre-existing nodes in…
We propose a continuum model for the degree distribution of directed networks in free and open-source software. The degree distributions of links in both the in-directed and out-directed dependency networks follow Zipf's law for the…
The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…
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…
We study the evolution of networks when the creation and decay of links are based on the position of nodes in the network measured by their centrality. We show that the same network dynamics arises under various centrality measures, and…
The organizational development of growing random networks is investigated. These growing networks are built by adding nodes successively and linking each to an earlier node of degree k with attachment probability A_k. When A_k grows slower…