Related papers: A Scale-free Network with Boolean Dynamics as a Fu…
We calculate the mean neighboring degree function $\bar k_{\rm{nn}}(k)$ and the mean clustering function $C(k)$ of vertices with degree $k$ as a function of $k$ in finite scale-free random networks through the static model. While both are…
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
We show that there are two classes of finite size effects for dynamic models taking place on a scale-free topology. Some models in finite networks show a behavior that depends only on the system size N. Others present an additional distinct…
There is increasing evidence that dense networks occur in on-line social networks, recommendation networks and in the brain. In addition to being dense, these networks are often also scale-free, i.e. their degree distributions follow…
Based on the empirical analysis of the dependency network in 18 Java projects, we develop a novel model of network growth which considers both: an attachment mechanism and the addition of new nodes with a heterogeneous distribution of their…
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 $j$…
We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys.…
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…
We introduce a model of information packet transport on networks in which the packets are posted by a given rate and move in parallel according to a local search algorithm. By performing a number of simulations we investigate the major…
This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N…
It is commonly believed that real networks are scale-free and fraction of nodes $P(k)$ with degree $k$ satisfies the power law $P(k) \propto k^{-\gamma} \text{ for } k > k_{min} > 0$. Preferential attachment is the mechanism that has been…
Recently, a novel model to describe ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ``+'' or ``-'', ``up'' or ``down'', ``yes'' or ``no''), still differing in…
We study statistical properties of a zero-range process (ZRP) on random networks. We derive an analytic expression for the distribution of particles (also called node occupation distribution) in the steady state of the ZRP in the ensemble…
We show that the connectivity distributions $P(k,t)$ of scale-free growing networks ($t$ is the network size) have the generic scale -- the cut-off at $k_{cut} \sim t^\beta$. The scaling exponent $\beta$ is related to the exponent $\gamma$…
Network growth is currently explained through mechanisms that rely on node prestige measures, such as degree or fitness. In many real networks those who create and connect nodes do not know the prestige values of existing nodes, but only…
In this paper we describe the emergence of scale-free degree distributions from statistical mechanics principles. We define an energy associated to a degree sequence as the logarithm of the number of indistinguishable simple networks it is…
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…
We consider the effects of network topology on the optimality of packet routing quantified by $\gamma_c$, the rate of packet insertion beyond which congestion and queue growth occurs. The key result of this paper is to show that for any…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections, and rewiring of existing links, we study {\em ad hoc} networks, where one also has to contend with rapid and…