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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…

Many realistic networks are scale-free, with small characteristic path lengths, high clustering, and power law in their degree distribution. They can be obtained by dynamical networks in which a preferential attachment process takes place.…

We propose a simple growing model for the evolution of small-world networks. It is introduced as a modified BA model in which all the edges connected to the new nodes are made locally to the creator and its nearest neighbors. It is found…

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…

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…

Most real complex networks -- such as protein interactions, social contacts, the internet -- are only partially known and available to us. While the process of exploring such networks in many cases resembles a random walk, it becomes a key…

We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power law distribution of degree, linear preferential attachment of new links and a negative…

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…

We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of…

A spatial scale-free network is introduced and studied whose motivation has been originated in the growing Internet as well as the Airport networks. We argue that in these real-world networks a new node necessarily selects one of its…

Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are…

The Asymmetric BA model extends the Barab\'asi-Albert scale-free network model by introducing a parameter $\omega$. As $\omega$ varies, the model transitions through different network structures: an extended lattice at $\omega = -1$, a…

Based on the concept and techniques of first-passage probability in Markov chain theory, this letter provides a rigorous proof for the existence of the steady-state degree distribution of the scale-free network generated by the…

A recent paper "Emergence of scaling in random networks" (cond-mat/9910332) by Barabasi and Albert proposes a growth mechanism to produce a stationary scale free distribution of the number of edges per node in large networks such as the…

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…

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…

Analytic solution for the average path length in a large class of uncorrelated random networks with hidden variables is found. We apply the approach to classical random graphs of Erdos and Renyi (ER), evolving networks introduced by…

We show that not only preferential attachment but also preferential depletion leads to scale-free networks. The resulting degree distribution exponents is typically less than two (5/3) as opposed to the case of the growth models studied…

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…

The sampling of scale-free networks in Molecular Biology is usually achieved by growing networks from a seed using recursive algorithms with elementary moves which include the addition and deletion of nodes and bonds. These algorithms…