Related papers: Critical Boolean networks with scale-free in-degre…
We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all…
Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the…
Based on a rigorous extension of classical statistical mechanics to networks, we study a specific microscopic network Hamiltonian. The form of this Hamiltonian is derived from the assumption that individual nodes increase/decrease their…
In this letter, we proposed an ungrowing scale-free network model, wherein the total number of nodes is fixed and the evolution of network structure is driven by a rewiring process only. In spite of the idiographic form of $G$, by using a…
Random Threshold Networks with sparse, asymmetric connections show complex dynamical behavior similar to Random Boolean Networks, with a transition from ordered to chaotic dynamics at a critical average connectivity $K_c$. In this type of…
We analyze the entropic equation of state for a many-particle interacting system in a scale-free network. The analysis is performed in terms of scaling functions which are of fundamental interest in the theory of critical phenomena and have…
Scale-free networks with small power law exponent are known to be robust, meaning that their qualitative topological structure cannot be altered by random removal of even a large proportion of nodes. By contrast, it has been argued in the…
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…
Generally, the threshold of percolation in complex networks depends on the underlying structural characterization. However, what topological property plays a predominant role is still unknown, despite the speculation of some authors that…
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…
Hierarchical models of scale free networks are introduced where numbers of nodes in clusters of a given hierarchy are stochastic variables. Our models show periodic oscillations of degree distribution P(k) in the log-log scale. Periods and…
The rate equations are used to study the scale-free behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices. An analysis of these equations shows that the degree…
Graphical models are a succinct way to represent the structure in probability distributions. This article analyzes the graphical model of nodal voltages in non-radial power distribution grids. Using algebraic and structural properties of…
We analyze the fine-grained connections between the average degree and the power-law degree distribution exponent in growing information networks. Our starting observation is a power-law degree distribution with a decreasing exponent and…
We give an exact solution for the complete distribution of component sizes in random networks with arbitrary degree distributions. The solution tells us the probability that a randomly chosen node belongs to a component of size s, for any…
Many complex networks in nature have directed links, a property that affects the network's navigability and large-scale topology. Here we study the percolation properties of such directed scale-free networks with correlated in- and…
We derive mean-field equations that describe the dynamics of a general model of rumor spreading on complex networks, and use analytical and numerical solutions of these equations to examine the threshold behavior and dynamics of the model…
Several studies on real complex networks from different fields as biology, economy, or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like $P(k)\approx…
We consider local leaders in random uncorrelated networks, i.e. nodes whose degree is higher or equal than the degree of all of their neighbors. An analytical expression is found for the probability of a node of degree $k$ to be a local…
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…