Related papers: Scale-free networks are rare
Scale-free networks are prevalently observed in a great variety of complex systems, which triggers various researches relevant to networked models of such type. In this work, we propose a family of growth tree networks $\mathcal{T}_{t}$,…
Metcalfe's Law captures the relationship between the value of a network and its scale, asserting that a network's value is directly proportional to the square of its size. Over the past four decades, various researchers have proposed…
Many complex systems, such as communication networks, display a surprising degree of robustness: while key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network.…
In this paper, we analyze the behavior of the global clustering coefficient in scale free graphs. We are especially interested in the case of degree distribution with an infinite variance, since such degree distribution is usually observed…
Many complex natural and physical systems exhibit patterns of interconnection that conform, approximately, to a network structure referred to as scale-free. Preferential attachment is one of many algorithms that have been introduced to…
Complex networks as the World Wide Web, the web of human sexual contacts or criminal networks often do not have an engineered architecture but instead are self-organized by the actions of a large number of individuals. From these local…
A complete understanding of real networks requires us to understand the consequences of the uneven interaction strengths between a system's components. Here we use the minimum spanning tree (MST) to explore the effect of weight assignment…
Many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. We show that these two features are the consequence of a hierarchical organization, implying that small…
The impact of inhomogeneous arrangement of nodes in space on network organization cannot be neglected in most of real-world scale-free networks. Here, we wish to suggest a model for a geographical network with nodes embedded in a fractal…
We investigate topologically biased failure in scale-free networks with degree distribution $P(k) \propto k^{-\gamma}$. The probability $p$ that an edge remains intact is assumed to depend on the degree $k$ of adjacent nodes $i$ and $j$…
Real-life networks often encounter vertex dysfunctions, which are usually followed by recoveries after appropriate maintenances. In this paper we present our research on a model of scale-free networks whose vertices are regularly removed…
We present a statistical mechanics approach for the description of complex networks. We first define an energy and an entropy associated to a degree distribution which have a geometrical interpretation. Next we evaluate the distribution…
Several kinds of walks on complex networks are currently used to analyze search and navigation in different systems. Many analytical and computational results are known for random walks on such networks. Self-avoiding walks (SAWs) are…
We study a modified version of a model previously proposed by Jackson and Wolinsky to account for communicating information and allocating goods in socioeconomic networks. In the model, the utility function of each node is given by a…
Here, we propose a class of scale-free networks $G(t;m)$ with some intriguing properties, which can not be simultaneously held by all the theoretical models with power-law degree distribution in the existing literature, including (i)…
Scale-free and non-computable characteristics of natural networks are found to result from the least-time dispersal of energy. To consider a network as a thermodynamic system is motivated since ultimately everything that exists can be…
Through the distinction between ``real'' and ``virtual'' links between the nodes of a graph, we develop a set of simple rules leading to scale-free networks with a tunable degree distribution exponent. Albeit sharing some similarities with…
It has been shown that many networks associated with complex systems are small-world (they have both a large local clustering coefficient and a small diameter) and they are also scale-free (the degrees are distributed according to a power…
We study a social network consisting of over $10^4$ individuals, with a degree distribution exhibiting two power scaling regimes separated by a critical degree $k_{\rm crit}$, and a power law relation between degree and local clustering. We…
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…