Related papers: General expression for the component size distribu…
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…
We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of "splitting" nodes of degree $k$ into $k$ nodes of degree 1. Four networks are considered, each…
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
The degree distribution is an important characteristic of complex networks. In many applications, quantification of degree distribution in the form of a fixed-length feature vector is a necessary step. On the other hand, we often need to…
We investigate the component sizes of the critical configuration model, as well as the related problem of critical percolation on a supercritical configuration model. We show that, at criticality, the finite third moment assumption on the…
We provide optimal rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our approach is to show that these distributions are unique fixed…
The configuration model was originally defined for undirected networks and has recently been extended to directed networks. Many empirical networks are however neither undirected nor completely directed, but instead usually partially…
We study the largest component of a random (multi)graph on n vertices with a given degree sequence. We let n tend to infinity. Then, under some regularity conditions on the degree sequences, we give conditions on the asymptotic shape of the…
Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are…
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 introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…
In this paper, we propose a general model for collaboration networks. Depending on a single free parameter "{\bf preferential exponent}", this model interpolates between networks with a scale-free and an exponential degree distribution. The…
We investigate a variety of statistical properties associated with the number of distinct degrees that exist in a typical network for various classes of networks. For a single realization of a network with N nodes that is drawn from an…
In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…
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…
Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a…
This paper studies the distribution of a family of rankings, which includes Google's PageRank, on a directed configuration model. In particular, it is shown that the distribution of the rank of a randomly chosen node in the graph converges…
Distributed configuration management is imperative for wireless infrastructureless networks where each node adjusts locally its physical and logical configuration through information exchange with neighbors. Two issues remain open. The…
Generalised degrees provide a natural bridge between local and global topological properties of networks. We define the generalised degree to be the number of neighbours of a node within one and two steps respectively. Tailored random graph…
The poster presents an analytic formalism describing metric properties of undirected random graphs with arbitrary degree distributions and statistically uncorrelated (i.e. randomly connected) vertices. The formalism allows to calculate the…