Related papers: Order statistics of observed network degrees

In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…

The degree distribution is a key statistical indicator in network theory, often used to understand how information spreads across connected nodes. In this paper, we focus on non-growing networks formed through a rewiring algorithm and…

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…

In this article, we study random graphs with a given degree sequence $d_1, d_2, \cdots, d_n$ from the configuration model. We show that under mild assumptions of the degree sequence, the spectral distribution of the normalized Laplacian…

The out-degree distribution of citation networks is investigated. Statistical data of the number of papers cited within a paper (out-degree) for different journals in the period 1991-1999 is reported. The out-degree distribution is…

The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…

We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the…

In this paper, we empirically investigate correlations among four centrality measures, originated from the social science, of various complex networks. For each network, we compute the centrality measures, from which the partial correlation…

While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be…

Gradient networks can be used to model the dominant structure of complex networks. Previous works have focused on random gradient networks. Here we study gradient networks that minimize jamming on substrate networks with scale-free and…

We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions in real-world networks. We first provide a rigorous definition of power-law distributions, equivalent to the definition of regularly varying…

The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional…

Many real networks feature the property of nestedness, i.e. the neighbours of nodes with a few connections are hierarchically nested within the neighbours of nodes with more connections. Despite the abstract simplicity of this notion,…

It was experimentally observed that the majority of real-world networks follow power law degree distribution. The aim of this paper is to study the algorithmic complexity of such "typical" networks. The contribution of this work is twofold.…

We derive a analytic evolution equation for overlap parameters including the effect of degree distribution on the transient dynamics of sequence processing neural networks. In the special case of globally coupled networks, the precisely…

The control and risk assessment in complex information systems require to take into account extremes arising from nodes with large node degrees. Various sampling techniques like a Page Rank random walk, a Metropolis-Hastings Markov chain…

The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable…

Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes. Such deletions include, for example, the failure of internet routers or…

It has been argued that the observed anticorrelation between the degrees of adjacent vertices in the network representation of the Internet has its origin in the restriction that no two vertices have more than one edge connecting them. Here…

The hidden variable formalism (based on the assumption of some intrinsic node parameters) turned out to be a remarkably efficient and powerful approach in describing and analyzing the topology of complex networks. Owing to one of its most…