Related papers: New exponential law for real networks
Social networks have increasingly become important and popular in modern times. Moreover, the influence of social networks plays a vital role in various organizations including government organizations, academic research or corporate…
We show that discrete distributions on the $d$-dimensional non-negative integer lattice can be approximated arbitrarily well via the marginals of stationary distributions for various classes of stochastic chemical reaction networks. We…
Husimi distributions and Wigner distributions are well-known quasi-probability distributions which appear in several contexts. In this paper, we show some remarkable aspects of these distribution functions related to geometric structures of…
In recent years, the study of Bell nonlocality has been generalized to quantum networks, where multiple independent sources distribute physical systems to distant parties who perform local measurements. In this context, a central open…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
A new protocol for quantum key distribution based on entanglement swapping is presented. In this protocol, both certain key and random key can be generated without any loss of security. It is this property differs our protocol from the…
The different between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law…
The generalized binomial distribution in Tsallis statistics (power-law system) is explicitly formulated from the precise $q$-Stirling's formula. The $\alpha $-divergence (or $q$-divergence) is uniquely derived from the generalized binomial…
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…
We investigate the degree distribution $P(k)$ and the clustering coefficient $C$ of the line graphs constructed on the Erd\"os-R\'enyi networks, the exponential and the scale-free growing networks. We show that the character of the degree…
In this paper we consider a well-known generalization of the Barab\'asi and Albert preferential attachment model - the Buckley-Osthus model. Buckley and Osthus proved that in this model the degree sequence has a power law distribution. As a…
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…
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…
The community structure and motif-modular-network hierarchy are of great importance for understanding the relationship between structures and functions. In this paper, we investigate the distribution of clique-degree, which is an extension…
To a considerable extent, the continuing importance and popularity of complex networks as models of real-world structures has been motivated by scale free degree distributions as well as the respectively implied hubs. Being related to…
Our primary objective in this paper is to study the distribution of the maximal clique size of the vertices in complex networks. We define the maximal clique size for a vertex as the maximum size of the clique that the vertex is part of and…
Universal scaling of distances between vertices of Erdos-Renyi random graphs, scale-free Barabasi-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A…
In this article we presented a brief study of the main network models with growth and preferential attachment. Such models are interesting because they present several characteristics of real systems. We started with the classical model…
For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are…
Many real networks share three generic properties: they are scale-free, display a small-world effect, and show a power-law strength-degree correlation. In this paper, we propose a type of deterministically growing networks called Sierpinski…