Related papers: Scale-free networks with exponent one
We have studied nucleation dynamics of the Ising model in scale-free networks with degree distribution $P(k)\sim k^{-\gamma}$ by using forward flux sampling method, focusing on how the network topology would influence the nucleation rate…
We obtain closed form expressions for the expected conditional degree distribution and the joint degree distribution of the linear preferential attachment model for network growth in the steady state. We consider the multiple-destination…
Recently, Broido & Clauset (2019) mentioned that (strict) Scale-Free networks were rare, in real life. This might be related to the statement of Stumpf, Wiuf & May (2005), that sub-networks of scale-free networks are not scale-free. In the…
As a fundamental structural transition in complex networks, core percolation is related to a wide range of important problems. Yet, previous theoretical studies of core percolation have been focusing on the classical Erd\H{o}s-R\'enyi…
We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…
We consider a stochastic model for directed scale-free networks following power-laws in the degree distributions in both incoming and outgoing directions. In our model, the number of vertices grow geometrically with time with growth rate p.…
Scale-free networks with moderate edge dependence experience a phase transition between ultrasmall and small world behaviour when the power law exponent passes the critical value of three. Moreover, there are laws of large numbers for the…
Complex networks have been mostly characterized from the point of view of the degree distribution of their nodes and a few other motifs (or modules), with a special attention to triangles and cliques. The most exotic phenomena have been…
The Japanese shareholding network at the end of March 2002 is studied. To understand the characteristics of this network intuitively, we visualize it as a directed graph and an adjacency matrix. Especially detailed features of networks…
Many real networks present a bounded scale-free behavior with a connectivity cut-off due to physical constraints or a finite network size. We study epidemic dynamics in bounded scale-free networks with soft and hard connectivity cut-offs.…
Deep connections are known to exist between scale-free networks and non-Gibbsian statistics. For example, typical degree distributions at the thermodynamical limit are of the form $P(k) \propto e_q^{-k/\kappa}$, where the $q$-exponential…
In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected…
One of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of…
We study the synchronization transition in scale-free networks that display power-law asymptotic behaviors in their degree distributions. The critical coupling strength and the order-parameter critical exponent derived by the mean field…
We propose a model to create synthetic networks that may also serve as a narrative of a certain kind of infrastructure network evolution. It consists of an initialization phase with the network extending tree-like for minimum cost and a…
Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance…
Self-similar networks with scale-free degree distribution have recently attracted much attention, since these apparently incompatible properties were reconciled in a paper by Song et al. by an appropriate box-counting method that enters the…
The concept of scale-free networks has been widely applied across natural and physical sciences. Many claims are made about the properties of these networks, even though the concept of scale-free is often vaguely defined. We present tools…
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…
Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of…