Related papers: Evolving Networks Created by Preferential Attachme…

We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of "splitting" nodes of degree $k$ into $k$ nodes of degree 1. Four networks are considered, each…

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…

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 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…

Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a high-degree expansion of the master equation, we…

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…

We introduce a new mechanism of connectivity evolution in networks to account for the emergence of scale-free behavior. The mechanism works on a fixed set of nodes and promotes growth from a minimally connected initial topology by the…

We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…

We prove almost sure convergence of the maximum degree in an evolving graph model combining a growing number of local choices with sublinear preferential attachment. At each step in the growth of the graph, a new vertex is introduced. Then…

When modeling a directed social network, one choice is to use the traditional preferential attachment model, which generates power-law tail distributions. In a traditional directed preferential attachment, every new edge is added…

Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential…

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 propose a model to create synthetic networks that may also serve as a narrative of a certain kind of infrastructure network evolution. It consists of an initialization phase with the network extending tree-like for minimum cost and a…

In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected…

This paper analyzes key properties of networks generated by geometric preferential attachment. We establish that the expected number of triangles is proportional to that of the standard preferential attachment model, with a proportionality…

We study the growth of a directed network, in which the growth is constrained by the cost of adding links to the existing nodes. We propose a new preferential-attachment scheme, in which a new node attaches to an existing node i with…

We present an evolving network model in which the total numbers of nodes and edges are conserved, but in which edges are continuously rewired according to nonlinear preferential detachment and reattachment. Assuming power-law kernels with…

The parallel computational complexity or depth of growing network models is investigated. The networks considered are generated by preferential attachment rules where the probability of attaching a new node to an existing node is given by a…

In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…

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…