Related papers: Scale-free Networks on Lattices

In this paper we theoretically and empirically study the degree and connectivity of the Internet's scale-free topology at the autonomous system (AS) level. The basic features of the scale-free network have influence on the normalization…

Recently, Broido & Clauset (2019) mentioned that (strict) Scale-Free networks were rare, in real life. This might be related to the statement of Stumpf, Wiuf & May (2005), that sub-networks of scale-free networks are not scale-free. In the…

Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete…

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 define the intrinsic scale at which a network begins to reveal its identity as the scale at which subgraphs in the network (created by a random walk) are distinguishable from similar sized subgraphs in a perturbed copy of the network. We…

The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…

We study a recent model of random networks based on the presence of an intrinsic character of the vertices called fitness. The vertices fitnesses are drawn from a given probability distribution density. The edges between pair of vertices…

Scale-free networks are a recently developed approach to model the interactions found in complex natural and man-made systems. Such networks exhibit a power-law distribution of node link (degree) frequencies n(k) in which a small number of…

Network embedding aims to learn low-dimensional representations of nodes in a network, while the network structure and inherent properties are preserved. It has attracted tremendous attention recently due to significant progress in…

We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power law distribution of degree, linear preferential attachment of new links and a negative…

We study the betweenness centrality of fractal and non-fractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality $C$ of nodes is much weaker in fractal network models…

We show that there are two classes of finite size effects for dynamic models taking place on a scale-free topology. Some models in finite networks show a behavior that depends only on the system size N. Others present an additional distinct…

We report on parallel observations in two seemingly unrelated areas of dynamical network research. The one is the so-called small world phenomenon and/or the observation of scale freeness in certain types of large (empirical) networks and…

A spatial network is constructed on a two dimensional space where the nodes are geometrical points located at randomly distributed positions which are labeled sequentially in increasing order of one of their co-ordinates. Starting with $N$…

The past two decades have seen significant successes in our understanding of complex networked systems, from the mapping of real-world social, biological and technological networks to the establishment of generative models recovering their…

We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the…

In this paper we generalize the concept of random networks to describe networks with non trivial features by a statistical mechanics approach. This framework is able to describe ensembles of undirected, directed as well as weighted…

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…

A network is scale-free if its connectivity density function is proportional to a power-law distribution. Scale-free networks may provide an explanation for the robustness observed in certain physical and biological phenomena, since the…

We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…