Related papers: Quantitative modeling of degree-degree correlation…
Multiplex networks are convenient mathematical representations for many real-world -- biological, social, and technological -- systems of interacting elements, where pairwise interactions among elements have different flavors. Previous…
Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…
We show that the load at each node in a preferential attachment network scales as a power of the degree of the node. For a network whose degree distribution is p(k) ~ k^(-gamma), we show that the load is l(k) ~ k^eta with eta = gamma - 1,…
Ever since the Barab\'{a}si-Albert (BA) scale-free network has been proposed, network modeling has been studied intensively in light of the network growth and the preferential attachment (PA). However, numerous real systems are featured…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…
We apply a Bethe-Peierls approach to statistical-mechanics models defined on random networks of arbitrary degree distribution and arbitrary correlations between the degrees of neighboring vertices. Using the NP-hard optimization problem of…
Despite the growing interest in characterizing the local geometry leading to the global topology of networks, our understanding of the local structure of complex networks, especially real-world networks, is still incomplete. Here, we…
Correlation between nodes is found to be a common and important property in many complex networks. Here we investigate degree correlations of the Barabasi-Albert (BA) Scale-Free model with both analytical results and simulations, and find…
Understanding the causes and effects of network structural features is a key task in deciphering complex systems. In this context, the property of network nestedness has aroused a fair amount of interest as regards ecological networks.…
Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order…
Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…
The Pearson correlation coefficient is commonly used for quantifying the global level of degree-degree association in complex networks. Here, we use a probabilistic representation of the underlying network structure for assessing the…
We study the mean length $\ell(k)$ of the shortest paths between a vertex of degree $k$ and other vertices in growing networks, where correlations are essential. In a number of deterministic scale-free networks we observe a power-law…
Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by…
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…
The purpose of this paper is to analyze the degree index and clustering index in random graphs. The degree index in our setup is a certain measure of degree irregularity whose basic properties are well studied in the literature, and the…
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…
Dynamical processes on complex networks such as information propagation, innovation diffusion, cascading failures or epidemic spreading are highly affected by their underlying topologies as characterized by, for instance, degree-degree…
A common way of classifying network connectivity is the association of the nodal degree distribution to specific probability distribution models. During the last decades, researchers classified many networks using the Poisson or Pareto…
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…