相关论文: Crossover from Scale-Free to Spatial Networks
We consider a one-dimensional network in which the nodes at Euclidean distance $l$ can have long range connections with a probabilty $P(l) \sim l^{-\delta}$ in addition to nearest neighbour connections. This system has been shown to exhibit…
Given a social network, which of its nodes have a stronger impact in determining its structure? More formally: which node-removal order has the greatest impact on the network structure? We approach this well-known problem for the first time…
Various real systems simultaneously exhibit scale-free and hierarchical structure. In this paper, we study analytically average distance in a deterministic scale-free network with hierarchical organization. Using a recursive method based on…
A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree $k$ follows a power law, decaying like $k^{-\alpha}$, often with $2 < \alpha < 3$. However,…
We discuss the behavior of large ensembles of phase oscillators networking via scale-free topologies in the presence of a positive correlation between the oscillators' natural frequencies and network's degrees. In particular, we show that…
Scale-free percolation is a percolation model on $\mathbb{Z}^d$ which can be used to model real-world networks. We prove bounds for the graph distance in the regime where vertices have infinite degrees. We fully characterize transience vs.…
Assortative mixing in networks is the tendency for nodes with the same attributes, or metadata, to link to each other. It is a property often found in social networks manifesting as a higher tendency of links occurring between people with…
Networks with underlying metric spaces attract increasing research attention in network science, statistical physics, applied mathematics, computer science, sociology, and other fields. This attention is further amplified by the current…
We discuss three related models of scale-free networks with the same degree distribution but different correlation properties. Starting from the Barabasi-Albert construction based on growth and preferential attachment we discuss two other…
We study diffusion (random walks) on recursive scale-free graphs, and contrast the results to similar studies in other analytically soluble media. This allows us to identify ways in which diffusion in scale-free graphs is special. Most…
A Barab\'asi-Albert scale-free network is constructed whose nodes are the Poisson distributed random points within a unit square and links are the straight line connections among the nodes. The cost function, which is the total wiring…
By employing a recently introduced optimization algorithm we explicitely design optimally synchronizable (unweighted) networks for any given scale-free degree distribution. We explore how the optimization process affects degree-degree…
We propose and analyze a stochastic model which explains, analytically, the cutoff behavior of real scale-free networks previously modeled computationally by Amaral et al. [Proc. Natl. Acad. Sci. U.S.A. 97, 11149 (2000)] and others. We…
The scale-free (SF) structure that commonly appears in many complex networks is one of the hot topics related to social, biological, and information sciences. The self-organized generation mechanisms are expected to be useful for efficient…
We address the problem of message transfer in a communication network. The network consists of nodes and links, with the nodes lying on a two dimensional lattice. Each node has connections with its nearest neighbours, whereas some special…
Like other social animals and biological systems, human groups constantly exchange information. Network models provide a way of quantifying this process by representing the pathways of information propagation between individuals. Existing…
One of the most important features of spatial networks such as transportation networks, power grids, Internet, neural networks, is the existence of a cost associated with the length of links. Such a cost has a profound influence on the…
Much recent research activity has been devoted to empirical study and theoretical models of complex networks (random graphs) with three qualitative features: power-law degree distribution, local clustering of edges, and small diameter. We…
We study the percolation phase transition in hierarchical scale-free nets. Depending on the method of construction, the nets can be fractal or small-world (the diameter grows either algebraically or logarithmically with the net size),…
We analyze the degree distribution's cut-off in finite size scale-free networks. We show that the cut-off behavior with the number of vertices $N$ is ruled by the topological constraints induced by the connectivity structure of the network.…