Related papers: Degree-degree distribution in a power law random i…
We introduce and study random bipartite networks with hidden variables. Nodes in these networks are characterized by hidden variables which control the appearance of links between node pairs. We derive analytic expressions for the degree…
We discuss a category of graphs, recursive clique trees, which have small-world and scale-free properties and allow a fine tuning of the clustering and the power-law exponent of their discrete degree distribution. We determine relevant…
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…
We show that an intricate relation of cluster properties and optimal bipartitions, which takes place in undirected random graphs, extends to directed and mixed random graphs. In particular, the satisfability threshold coincides with the…
We investigate the degree sequences of geometric preferential attachment graphs in general compact metric spaces. We show that, under certain conditions on the attractiveness function, the behaviour of the degree sequence is similar to that…
The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in…
In this paper, a random clique network model to mimic the large clustering coefficient and the modular structure that exist in many real complex networks, such as social networks, artificial networks, and protein interaction networks, is…
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…
Random graphs with power-law degrees can model scale-free networks as sparse topologies with strong degree heterogeneity. Mathematical analysis of such random graphs proved successful in explaining scale-free network properties such as…
Spatial random graphs capture several important properties of real-world networks. We prove quenched results for the continuum space version of scale-free percolation introduced in [DW18]. This is an undirected inhomogeneous random graph…
A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form…
This paper presents an approach to the modeling of degree-degree correlation in complex networks. Thus, a simple function, \Delta(k', k), describing specific degree-to- degree correlations is considered. The function is well suited to…
Delaunay triangulation can be considered as a type of complex networks. For complex networks, the degree distribution is one of the most important inherent characteristics. In this paper, we first consider the two- and three-dimensional…
In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edges are far from independent, and to prove several results…
Introduced recently, the concept of hierarchical degree allows a more complete characterization of the topological context of a node in a complex network than the traditional node degree. This article presents analytical characterization…
We discuss two sampling schemes for selecting random subnets from a network: Random sampling and connectivity dependent sampling, and investigate how the degree distribution of a node in the network is affected by the two types of sampling.…
We derive properties of Latent Variable Models for networks, a broad class of models that includes the widely-used Latent Position Models. These include the average degree distribution, clustering coefficient, average path length and degree…
We conjecture that the distribution of the edge-disjoint union of two random regular graphs on the same vertex set is asymptotically equivalent to a random regular graph of the combined degree, provided it grows as the number of vertices…
This article discusses the properties of extremes of degree sequences calculated from network data. We introduce the notion of a normalized degree, in order to permit a comparison of degree sequences between networks with differing numbers…
Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the…