Related papers: Beyond the Steady-State: Analytical Study of Netwo…

Many networks exhibit scale free behavior where their degree distribution obeys a power law for large vertex degrees. Models constructed to explain this phenomena have relied on preferential attachment where the networks grow by the…

In several real-world networks like the Internet, WWW etc., the number of links grow in time in a non-linear fashion. We consider growing networks in which the number of outgoing links is a non-linear function of time but new links between…

Approaches from statistical physics are applied to investigate the structure of network models whose growth rules mimic aspects of the evolution of the world-wide web. We first determine the degree distribution of a growing network in which…

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…

In many real world networks, the number of links increases nonlinearly with the number of nodes. Models of such accelerated growth have been considered earlier with deterministic and stochastic number of links. Here we consider stochastic…

We study the role of finiteness and fluctuations about average quantities for basic structural properties of growing networks. We first determine the exact degree distribution of finite networks by generating function approaches. The…

The question is: What does happen to the real-world networks which cause them not to grow permanently? The idea here is that real-world networks have to pay the cost of growth. We investigate the growth and trade-off between value and cost…

In this work, a growing network model that can generate a random network with finite degree in infinite time is studied. The dynamics are governed by a rule where the degree increases under a scheme similar to the Malthus-Verhulst model in…

The Master equation describes the time evolution of the probabilities of a system with a discrete state space. This time evolution approaches for long times a stationary state that will in general depend on the initial probability…

The degree distribution is a key statistical indicator in network theory, often used to understand how information spreads across connected nodes. In this paper, we focus on non-growing networks formed through a rewiring algorithm and…

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…

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…

Preferential attachment drives the evolution of many complex networks. Its analytical studies mostly consider the simplest case of a network that grows uniformly in time despite the accelerating growth of many real networks. Motivated by…

We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…

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…

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…

Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular,…

We give an intuitive though general explanation of the finite-size effect in scale-free networks in terms of the degree distribution of the starting network. This result clarifies the relevance of the starting network in the final degree…

Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great…

We generalize the poissonian evolving random graph model of Bauer and Bernard to deal with arbitrary degree distributions. The motivation comes from biological networks, which are well-known to exhibit non poissonian degree distribution. A…