Related papers: The Fractional Preferential Attachment Scale-Free …

The network properties of a graph ensemble subject to the constraints imposed by the expected degree sequence are studied. It is found that the linear preferential attachment is a fundamental rule, as it keeps the maximal entropy in sparse…

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 that generates a new class of networks exhibiting power-law degree distribution with a spectrum of exponents depending on the number of links ($m$) with which incoming nodes join the existing network. Unlike the…

Preferential attachment is often suggested to be the underlying mechanism of the growth of a network, largely due to that many real networks are, to a certain extent, scale-free. However, such attribution is usually made under debatable…

Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…

Scale-free networks are characterized by a degree distribution with power-law behavior and have been shown to arise in many areas, ranging from the World Wide Web to transportation or social networks. Degree distributions of observed…

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 present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…

Ever since the Barab\'{a}si-Albert (BA) scale-free network has been proposed, network modeling has been studied intensively in light of the network growth and the preferential attachment (PA). However, numerous real systems are featured…

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…

There is a complex relation between the mechanism of preferential attachment, scale-free degree distributions and hyperbolicity in complex networks. In fact, both preferential attachment and hidden hyperbolic spaces often generate…

In this paper we present a framework for the extension of the preferential attachment (PA) model to heterogeneous complex networks. We define a class of heterogeneous PA models, where node properties are described by fixed states in an…

Preferential attachment models are a common class of graph models which have been used to explain why power-law distributions appear in the degree sequences of real network data. One of the things they lack, however, is higher-order network…

The Barab\'asi-Albert model is a popular scheme for creating scale-free graphs but has been previously shown to have ambiguities in its definition. In this paper we discuss a new ambiguity in the definition of the BA model by identifying…

The percolation threshold of the network model by Barabasi and Albert (BA-model) [Science 286, 509 (1999)] has thus far only been 'guessed' based on simulations and comparison with other models. Due to the still uncertain influence of…

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…

Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the…

Many complex systems--from social and communication networks to biological networks and the Internet--are thought to exhibit scale-free structure. However, prevailing explanations rely on the constant addition of new nodes, an assumption…

Many real-world networks have properties of small-world networks, with clustered local neighborhoods and low average-shortest path (ASP). They may also show a scale-free degree distribution, which can be generated by growth and preferential…

Scale-free networks are quite popular nowadays since many systems are well represented by such structures. In order to study these systems, several models were proposed. However, most of them do not take into account the node-to-node…