Related papers: Degrees in Preferential Attachment Networks with a…
In this paper, we first discuss the origin of preferential attachment. Then we establish the generalized preferential attachment which has two new properties; first, it encapsulates both the topological and weight aspects of a network,…
We consider a preferential attachment random graph with self-reinforcement. Each time a new vertex comes in, it attaches itself to an old vertex with a probability that is proportional to the sum of the degrees of that old vertex at all…
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…
Preferential attachment models form a popular class of growing networks, where incoming vertices are preferably connected to vertices with high degree. We consider a variant of this process, where vertices are equipped with a random initial…
Network models with preferential attachment, where new nodes are injected into the network and form links with existing nodes proportional to their current connectivity, have been well studied for some time. Extensions have been introduced…
We investigate choice-driven network growth. In this model, nodes are added one by one according to the following procedure: for each addition event a set of target nodes is selected, each according to linear preferential attachment, and a…
We highlight intriguing features of complex networks that are grown by \emph{redirection}. In this mechanism, a target node is chosen uniformly at random from the pre-existing network nodes and the new node attaches either to this initial…
In this article we presented a brief study of the main network models with growth and preferential attachment. Such models are interesting because they present several characteristics of real systems. We started with the classical model…
We propose a preferential attachment model for network growth where new entering nodes have a partial information about the state of the network. Our main result is that the presence of bounded information modifies the degree distribution…
Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…
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…
Preferential attachment models have been widely studied in complex networks, because they can explain the formation of many networks like social networks, citation networks, power grids, and biological networks, to name a few. Motivated by…
The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment…
We find assimpotics for the first $k$ highest degrees of the degree distribution in an evolving tree model combining the local choice and the preferential attachment. In the considered model, the random graph is constructd in the following…
The linear preferential attachment hypothesis has been shown to be quite successful to explain the existence of networks with power-law degree distributions. It is then quite important to determine if this mechanism is the consequence of a…
Many important real-world networks manifest "small-world" properties such as scale-free degree distributions, small diameters, and clustering. The most common model of growth for these networks is "preferential attachment", where nodes…
Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment…
We analyze a dynamic random undirected graph in which newly added vertices are connected to those already present in the graph either using, with probability $p$, an anti-preferential attachment mechanism or, with probability $1-p$, a…
There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied.…
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…