Related papers: Typical distances in the directed configuration mo…
We study directed random graphs (random graphs whose edges are directed) as they evolve in discrete time by the addition of nodes and edges. For two distinct evolution strategies, one that forces the graph to a condition of near acyclicity…
We consider the strongly connected components (SCCs) of a uniform directed graph on $n$ vertices with i.i.d. in- and out-degree pairs distributed as $(D^-,D^+)$, with $\mathbb E[D^+]=\mathbb E[D^-]=\mu$. We condition on equal total in- and…
Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…
We study the distribution of diameters d of Erd\"os-R\'enyi random graphs with average connectivity c. The diameter d is the maximum among all shortest distances between pairs of nodes in a graph and an important quantity for all dynamic…
Pairwise comparison of graphs is key to many applications in Machine learning ranging from clustering, kernel-based classification/regression and more recently supervised graph prediction. Distances between graphs usually rely on…
Findings: We show that the distance distribution in an undirected network Lorenz majorizes the one of a chain. As a consequence, the average and median distances in any such network are smaller than or equal to those of a chain. Research…
We study the long range percolation model on $\mathbb{Z}$ where sites $i$ and $j$ are connected with probability $\beta |i-j|^{-s}$. Graph distances are now well understood for all exponents $s$ except in the case $s=2$ where the model…
Bidirected graphs generalize directed and undirected graphs in that edges are oriented locally at every node. The natural notion of the degree of a node that takes into account (local) orientations is that of net-degree. In this paper, we…
We consider a stochastic directed graph on the integers whereby a directed edge between $i$ and a larger integer $j$ exists with probability $p_{j-i}$ depending solely on the distance between the two integers. Under broad conditions, we…
Universal scaling of distances between vertices of Erdos-Renyi random graphs, scale-free Barabasi-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A…
Let \( D \) be a strongly connected digraph. The average distance of a vertex \( v \) in \( D \) is defined as the arithmetic mean of the distances from \( v \) to all other vertices in \( D \). The remoteness \( \rho(D) \) of \( D \) is…
Scale-free percolation is a stochastic model for complex networks. In this spatial random graph model, vertices $x,y\in\mathbb{Z}^d$ are linked by an edge with probability depending on i.i.d.\ vertex weights and the Euclidean distance…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
We introduce an algorithm that constructs a random uniform graph with prescribed degree sequence together with a depth first exploration of it. In the so-called supercritical regime where the graph contains a giant component, we prove that…
We find Gaussian cutoff profiles for the total variation distance to stationarity of a random walk on a multiplex network: a finite number of directed configuration models sharing a vertex set, each with its own bounded degree distribution…
Recently, the classical configuration model for random graphs with given degree distribution has been extensively used as a null model in contraposition to real networks with the same degree distribution. In this paper, we briefly review…
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…
We consider an edge-weighted uniform random graph with a given degree sequence (Repeated Configuration Model) which is a useful approximation for many real-world networks. It has been observed that the vertices which are separated from the…
Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…
We present analytical results for the distribution of shortest path lengths between random pairs of nodes in configuration model networks. The results, which are based on recursion equations, are shown to be in good agreement with numerical…