Related papers: Construction of Directed Assortative Configuration…

The focus of this work is on estimation of the in-degree distribution in directed networks from sampling network nodes or edges. A number of sampling schemes are considered, including random sampling with and without replacement, and…

We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify…

Graph convolutional networks have been successful in addressing graph-based tasks such as semi-supervised node classification. Existing methods use a network structure defined by the user based on experimentation with fixed number of layers…

A network's assortativity is the tendency of vertices to bond with others based on similarities, usually excess vertex degree. In this paper we consider assortativity in weighted networks, both directed and undirected. To this end, we…

The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…

By natural way the hierarchy structure is introduced on directed graphs with weighted adjacencies. Embedded system of algebras of subsets of the set of vertices of such digraph and it's consolidations, which vertices are the elementary sets…

Graph-structured data ubiquitously appears in science and engineering. Graph neural networks (GNNs) are designed to exploit the relational inductive bias exhibited in graphs; they have been shown to outperform other forms of neural networks…

We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated…

We introduce, and analyze, three measures for degree-degree dependencies, also called degree assortativity, in directed random graphs, based on Spearman's rho and Kendall's tau. We proof statistical consistency of these measures in general…

In this paper we consider the directed path-width and directed tree-width of recursively defined digraphs. As an important combinatorial tool, we show how the directed path-width and the directed tree-width can be computed for the disjoint…

We analyze the distribution of the distance between two nodes, sampled uniformly at random, in digraphs generated via the directed configuration model, in the supercritical regime. Under the assumption that the covariance between the…

Canonical orderings serve as the basis for many incremental planar drawing algorithms. All these techniques, however, have in common that they are limited to undirected graphs. While $st$-orderings do extend to directed graphs, especially…

We study the growth of bipartite networks in which the number of nodes in one of the partitions is kept fixed while the other partition is allowed to grow. We study random and preferential attachment as well as combination of both. We…

We define gradient networks as directed graphs formed by local gradients of a scalar field distributed on the nodes of a substrate network G. We derive an exact expression for the in-degree distribution of the gradient network when the…

Graphs are called navigable if one can find short paths through them using only local knowledge. It has been shown that for a graph to be navigable, its construction needs to meet strict criteria. Since such graphs nevertheless seem to…

A variety of statistical graphical models have been defined to represent the conditional independences underlying a random vector of interest. Similarly, many different graphs embedding various types of preferential independences, as for…

We provide algorithms involving edge slides, for a connected simple graph to evolve in a finite number of steps to another connected simple graph in a prescribed configuration, and for the regularization of such a graph by the minimization…

This study introduces an algorithm that generates undirected graphs with three main characteristics of real-world networks: scale-freeness, short distances between nodes (small-world phenomenon), and large clustering coefficients. The main…

In statistical mechanical investigations on complex networks, it is useful to employ random graphs ensembles as null models, to compare with experimental realizations. Motivated by transcription networks, we present here a simple way to…

We address here the problem of generating random graphs uniformly from the set of simple connected graphs having a prescribed degree sequence. Our goal is to provide an algorithm designed for practical use both because of its ability to…