Related papers: Giant strongly connected component of directed net…

We describe the complex global structure of giant components in directed multiplex networks which generalizes the well-known bow-tie structure, generic for ordinary directed networks. By definition, a directed multiplex network contains…

Random K-out graphs, denoted $\mathbb{H}(n;K)$, are generated by each of the $n$ nodes drawing $K$ out-edges towards $K$ distinct nodes selected uniformly at random, and then ignoring the orientation of the arcs. Recently, random K-out…

Recently, the first author showed that the giant in random undirected graphs is `almost' local. This means that, under a necessary and sufficient condition, the limiting proportion of vertices in the giant converges in probability to the…

A directed graph G (V, E) is strongly connected if and only if, for a pair of vertices X and Y from V, there exists a path from X to Y and a path from Y to X. In Computer Science, the partition of a graph in strongly connected components is…

Random K-out graphs are receiving attention as a model to construct sparse yet well-connected topologies in distributed systems including sensor networks, federated learning, and cryptocurrency networks. In response to the growing…

If we pick $n$ random points uniformly in $[0,1]^d$ and connect each point to its $k-$nearest neighbors, then it is well known that there exists a giant connected component with high probability. We prove that in $[0,1]^d$ it suffices to…

Consider a random directed graph on $n$ vertices with independent identically distributed outdegrees with distribution $F$ having mean $\mu$, and destinations of arcs selected uniformly at random. We show that if $\mu >1$ then for large $n$…

We study site and bond percolation on directed simple random graphs with a given degree distribution and derive the expressions for the critical value of the percolation probability above which the giant strongly connected component emerges…

Stochastic Kronecker graphs are a model for complex networks where each edge is present independently according the Kronecker (tensor) product of a fixed matrix k-by-k matrix P with entries in [0,1]. We develop a novel correspondence…

Random K-out graphs are garnering interest in designing distributed systems including secure sensor networks, anonymous crypto-currency networks, and differentially-private decentralized learning. In these security-critical applications, it…

This work presents exact expressions for size distributions of weak/multilayer connected components in two generalisations of the configuration model: networks with directed edges and multiplex networks with arbitrary number of layers. The…

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 the study of \textit{randomly oriented divisor graphs}. For each $\rho \in [0,1]$, the randomly oriented divisor graph $\mathcal{D}_\rho(N)$ is obtained from the divisor graph on $\{1, 2, \ldots, N\}$ by directing each edge…

Directed graphs are widely used in modelling of nonsymmetric relations in various sciences and engineering disciplines. We discuss invariants of strongly connected directed graphs - minimal number of vertices or edges necessary to remove to…

We study the problem of the existence of a giant component in a random multipartite graph. We consider a random multipartite graph with $p$ parts generated according to a given degree sequence $n_i^{\mathbf{d}}(n)$ which denotes the number…

We study directed random graphs (random graphs whose edges are directed), and present new results on the so-called strong components of those graphs. We provide analytic and simulation results on two special classes of strong component,…

We analyze the stability of the network's giant connected component under impact of adverse events, which we model through the link percolation. Specifically, we quantify the extent to which the largest connected component of a network…

Scale-free networks arise from power-law degree distributions. Due to the finite size of real-world networks, the power law inevitably has a cutoff at some maximum degree $\Delta$. We investigate the relative size of the giant component $S$…

Various different random graph models have been proposed in which the vertices of the graph are seen as members of a metric space, and edges between vertices are determined as a function of the distance between the corresponding metric…

The micro-structure of the giant component of the Erd{\H o}s-R\'enyi network and other configuration model networks is analyzed using generating function methods. While configuration model networks are uncorrelated, the giant component…