Related papers: Degree-degree distribution in a power law random i…
Large real-world graphs tend to be sparse, but they often contain many densely connected subgraphs and exhibit high clustering coefficients. While recent random graph models can capture this sparsity, they ignore the local density, or vice…
We present a detailed analysis of the Connecting Nearest Neighbors (CNN) model by V\'azquez. We show that the degree distribution follows a power law, but the scaling exponent can vary with the parameter setting. Moreover, the…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
We consider the extremal values of the stationary distribution of sparse directed random graphs with given degree sequences and their relation to the extremal values of the in-degree sequence. The graphs are generated by the directed…
We find assimpotics for the first $k$ highest degrees of the degree distribution in an evolving tree model combining the local choice and the preferential attachment. In the considered model, the random graph is constructd in the following…
The purpose of this paper is to assess the statistical characterization of weighted networks in terms of the generalization of the relevant parameters, namely average path length, degree distribution and clustering coefficient. Although the…
The global clustering coefficient is an effective measure for analyzing and comparing the structures of complex networks. The random annulus graph is a modified version of the well-known Erd\H{o}s-R\'{e}nyi random graph. It has been…
One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…
We derive exact equations for the spectral density of sparse networks with an arbitrary distribution of the number of single edges and triangles per node. These equations enable a systematic investigation of the effect of clustering on the…
Inhomogeneity in networks can be detected by the analysis of the correlation of the total degree of nearest neighbors. This is illustrated by two models. The first one is a random multi-partitions network that the Aboav Weaire law, which…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
Even though power-law or close-to-power-law degree distributions are ubiquitously observed in a great variety of large real networks, the mathematically satisfactory treatment of random power-law graphs satisfying basic statistical…
We describe the asymptotic behaviour of large degrees in random hyperbolic graphs, for all values of the curvature parameter $ \alpha$. We prove that, with high probability, the node degrees satisfy the following ordering property: the…
The graph theoretic properties of the clustering coefficient, characteristic (or average) path length, global and local efficiency, provide valuable information regarding the structure of a graph. These four properties have applications to…
We study the random graph G_{n,\lambda/n} conditioned on the event that all vertex degrees lie in some given subset S of the non-negative integers. Subject to a certain hypothesis on S, the empirical distribution of the vertex degrees is…
The goal of is to study how increased variability in the degree distribution impacts the global connectivity properties of a large network. We approach this question by modeling the network as a uniform random graph with a given degree…
In this paper we study the degree sequence of the permutation graph $G_{\pi_n}$ associated with a sequence $\pi_n\in S_n$ of random permutations. Joint limiting distributions of the degrees are established using results from graph and…
In this work we explore degree assortativity in complex networks, and extend its usual definition beyond that of nearest neighbours. We apply this definition to model networks, and describe a rewiring algorithm that induces assortativity.…
Many weighted scale-free networks are known to have a power-law correlation between strength and degree of nodes, which, however, has not been well explicated. We investigate the dynamic behaviors of resource/traffic flow on scale-free…
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…