Related papers: Are Barabasi-Albert networks self-averaging?
In the consensus model with bounded confidence, studied by Deffuant et al. (2000), two randomly selected people who differ not too much in their opinion both shift their opinions towards each other. Now we restrict this exchange of…
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 give exact relations for certain types of the hierarchic fractal structures. In the blatant distinction from regular networks of the "small world" (SW) topology [1], regular fractal networks manifests the logarithmic dependence of the…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
We analyze about two hundred naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned…
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.…
We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering,…
This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. We analyze several…
We generalize the scale-free network model of Barab\`asi and Albert [Science 286, 509 (1999)] by proposing a class of stochastic models for scale-free interdependent networks in which interdependent nodes are not randomly connected but…
We give an intuitive though general explanation of the finite-size effect in scale-free networks in terms of the degree distribution of the starting network. This result clarifies the relevance of the starting network in the final degree…
Most real complex networks -- such as protein interactions, social contacts, the internet -- are only partially known and available to us. While the process of exploring such networks in many cases resembles a random walk, it becomes a key…
A network is formed using the $N$ sites of an one-dimensional lattice in the shape of a ring as nodes and each node with the initial degree $k_{in}=2$. $N$ links are then introduced to this network, each link starts from a distinct node,…
With the evolution of social networks, the network structure shows dynamic nature in which nodes and edges appear as well as disappear for various reasons. The role of a node in the network is presented as the number of interactions it has…
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…
In this paper, firstly, we study analytically the topological features of a family of hierarchical lattices (HLs) from the view point of complex networks. We derive some basic properties of HLs controlled by a parameter $q$. Our results…
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 investigate the influence of the network's size on the degree distribution in Barabasi-Albert model of growing network with initial attractiveness. Our approach based on spectral moments allows to treat analytically several variants of…
In complex systems, responses to small perturbations are too diverse to predict how much they would be definitely, and then such diverse responses can be predicted in a probabilistic way. Here we study such a problem in scale-free networks,…
We study Erd\"{o}s-R\'enyi random graphs with random weights associated with each link. We generate a new ``Supernode network'' by merging all nodes connected by links having weights below the percolation threshold (percolation clusters)…
With a simple attack and repair evolution model, we investigate and compare the stability of the Erdos-Renyi random graphs (RG) and Barabasi-Albert scale-free (SF) networks. We introduce a new quantity, invulnerability I(s), to describe the…