Related papers: Are Barabasi-Albert networks self-averaging?
Analytic solution for the average path length in a large class of random graphs is found. We apply the approach to classical random graphs of Erd\"{o}s and R\'{e}nyi (ER) and to scale-free networks of Barab\'{a}si and Albert (BA). In both…
The rise and fall of online social networks recently generated an enormous amount of interest among people, both inside and outside of academia. Gillette [Businessweek magazine, 2011] did a detailed analysis of MySpace, which started losing…
Earthquake network is known to be complex in the sense that it is scale-free, small-world, hierarchically organized and assortatively mixed. Here, the time evolution of earthquake network is analyzed around main shocks in the context of the…
In this paper, we propose a simple rule that generates scale-free small-world networks with tunable assortative coefficient. These networks are constructed by two-stage adding process for each new node. The model can reproduce scale-free…
Many biological, ecological and economic systems are best described by weighted networks, as the nodes interact with each other with varying strength. However, most network models studied so far are binary, the link strength being either 0…
Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be…
One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g., patents) scale nonlinearly with the population~x of the cities in which they appear, i.e., $y\sim x^\beta, \beta \neq 1$. More…
We prove that the treewidth of an Erd\"{o}s-R\'{e}nyi random graph $\rg{n, m}$ is, with high probability, greater than $\beta n$ for some constant $\beta > 0$ if the edge/vertex ratio $\frac{m}{n}$ is greater than 1.073. Our lower bound…
We consider the self organizing process of merging and regeneration of vertices in complex networks and demonstrate that a scale-free degree distribution emerges in a steady state of such a dynamics. The merging of neighbor vertices in a…
Small-world and scale-free networks are known to be more easily synchronized than regular lattices, which is usually attributed to the smaller network distance between oscillators. Surprisingly, we find that networks with a homogeneous…
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…
It is suggested that the degree distribution for networks of the cell-metabolism for simple organisms reflects an ubiquitous randomness. This implies that natural selection has exerted no or very little pressure on the network degree…
We study the dynamics of the Internet topology based on the empirical data on the level of the autonomous systems. It is found that the fluctuations occurring in the stochastic process of connecting and disconnecting edges are important…
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,…
Co-evolution exhibited by a network system, involving the intricate interplay between the dynamics of the network itself and the subsystems connected by it, is a key concept for understanding the self-organized, flexible nature of…
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…
Network growth as described by the Duplication-Divergence model proposes a simple general idea for the evolution dynamics of natural networks. In particular it is an alternative to the well known Barab\'asi-Albert model when applied to…
The vast majority of real-world networks are scale-free, loopy, and sparse, with a power-law degree distribution and a constant average degree. In this paper, we study first-order consensus dynamics in binary scale-free networks, where…
1. Basic constructions. 2. Equilibrium and nonequilibrium networks. 3. Equilibrium uncorrelated networks. 4. Nonequilibrium nongrowing scale-free nets. 5. Types of correlations. 6. When pair correlations are important. 7. When loops are…
Several studies have found that collaboration networks are scale-free, proposing that such networks can be modeled by specific network evolution mechanisms like preferential attachment. This study argues that collaboration networks can look…