Related papers: Nonlinear Barab\'asi-Albert Network
The $\boldsymbol{\beta}$-model for random graphs is commonly used for representing pairwise interactions in a network with degree heterogeneity. Going beyond pairwise interactions, Stasi et al. (2014) introduced the hypergraph…
We present analytical results for the emerging structure of networks that evolve via a combination of growth (by node addition and random attachment) and contraction (by random node deletion). To this end we consider a network model in…
The performance of the Hopfield neural network model is numerically studied on various complex networks, such as the Watts-Strogatz network, the Barab{\'a}si-Albert network, and the neuronal network of the C. elegans. Through the use of a…
This paper presents the development of a new class of algorithms that accurately implement the preferential attachment mechanism of the Barab\'asi-Albert (BA) model to generate scale-free graphs. Contrary to existing approximate…
Self-organization of robust and efficient networks is important for a future design of communication or transportation systems, because both characteristics are not coexisting in many real networks. As one of the candidates for the…
Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…
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…
Based on the empirical analysis of the dependency network in 18 Java projects, we develop a novel model of network growth which considers both: an attachment mechanism and the addition of new nodes with a heterogeneous distribution of their…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
In this article, we show that if each node of the Barab\'{a}si-Albert (BA) network is characterized by the generalized degree $q$, i.e. the product of their degree $k$ and the square root of their respective birth time, then the…
Network models with preferential attachment, where new nodes are injected into the network and form links with existing nodes proportional to their current connectivity, have been well studied for some time. Extensions have been introduced…
The average node-to-node distance of scale-free graphs depends logarithmically on N, the number of nodes, while the probability distribution function (pdf) of the distances may take various forms. Here we analyze these by considering…
We investigate the degree-degree correlations in the Erdos-Renyi networks, the growing exponential networks and the scale-free networks. We demonstrate that these correlations are the largest for the exponential networks. We calculate also…
The preferential attachment model is a natural and popular random graph model for a growing network that contains very well-connected ``hubs''. We study the higher-order connectivity of such a network by investigating the topological…
Assortativity, i.e. the tendency of a vertex to bond with another based on their similarity, such as degree, is an important network characteristic that is well-known to be relevant for the network's robustness against attacks. Commonly it…
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…
We propose an extended local-world evolving network model including a triad formation step. In the process of network evolution, random fluctuation in the number of new edges is involved. We derive analytical expressions for degree…
We introduce a general deterministic model for Apollonian Networks in an iterative fashion. The networks have small-world effect and scale-free topology. We calculate the exact results for the degree exponent, the clustering coefficient and…
A network growth mechanism based on a two-step preferential rule is investigated as a model of network growth in which no global knowledge of the network is required. In the first filtering step a subset of fixed size $m$ of existing nodes…
We propose a generalization of the concept of assortativity based on the tensorial representation of multilayer networks, covering the definitions given in terms of Pearson and Spearman coefficients. Our approach can also be applied to…