Related papers: The degree-restricted random process is far from u…

For a fixed degree sequence $\mathcal{D}=(d_1,...,d_n)$, let $G(\mathcal{D})$ be a uniformly chosen (simple) graph on $\{1,...,n\}$ where the vertex $i$ has degree $d_i$. In this paper we determine whether $G(\mathcal{D})$ has a giant…

We introduce and analyse a Dynamic Random Graph with Vertex Removal (DRGVR) defined as follows. At every step, with probability $p > 1/2$ a new vertex is introduced, and with probability $1-p$ a vertex, chosen uniformly at random among the…

Consider a random multigraph G* with given vertex degrees d_1,...,d_n, contructed by the configuration model. We show that, asymptotically for a sequence of such multigraphs with the number of edges (d_1+...+d_n)/2 tending to infinity, the…

Causal discovery aims to recover a causal graph from data generated by it; constraint based methods do so by searching for a d-separating conditioning set of nodes in the graph via an oracle. In this paper, we provide analytic evidence that…

Let $[\mathcal{P}]$ be the points of a Poisson process on $\mathbb{R}^d$ and $F$ a probability distribution with support on the non-negative integers. Models are formulated for generating translation invariant random graphs with vertex set…

We introduce a new random graph model motivated by biological questions relating to speciation. This random graph is defined as the stationary distribution of a Markov chain on the space of graphs on $\{1, \ldots, n\}$. The dynamics of this…

We prove that the restriction of the vertex-reinforced jump process to a subset of the vertex set is a mixture of vertex-reinforced jump processes. A similar statement holds for the non-linear hyperbolic supersymmetric sigma model. This is…

For an arbitrary initial configuration of discrete loads over vertices of a distributed graph, we consider the problem of minimizing the {\em discrepancy} between the maximum and minimum loads among all vertices. For this problem, this…

We introduce a process where a connected rooted multigraph evolves by splitting events on its vertices, occurring randomly in continuous time. When a vertex splits, its incoming edges are randomly assigned between its offspring and a…

Let $F$ be a probability distribution with support on the non-negative integers. Two algorithms are described for generating a stationary random graph, with vertex set $\mathbb{Z}$, so that the degrees of the vertices are i.i.d.\ random…

This Master's thesis examines the properties of large degree vertices in random recursive directed acyclic graphs (RRDAGs), a generalization of the well-studied random recursive tree (RRT) model. Using a novel adaptation of Kingman's…

In this work we consider a growing random graph sequence where a new vertex is less likely to join to an existing vertex with high degree and more likely to join to a vertex with low degree. In contrast to the well studied…

Degree sequence (DS) problems are around for at least hundred twenty years, and with the advent of network science, more and more complicated, structured DS problems were invented. Interestingly enough all those problems so far are…

We study the random graph obtained by random deletion of vertices or edges from a random graph with given vertex degrees. A simple trick of exploding vertices instead of deleting them, enables us to derive results from known results for…

Given two distributions F and G on the nonnegative integers we propose an algorithm to construct in- and out-degree sequences from samples of i.i.d. observations from F and G, respectively, that with high probability will be graphical, that…

Real-world networks evolve over time via additions or removals of vertices and edges. In current network evolution models, vertex degree varies or grows arbitrarily. A recently introduced degree-preserving network growth (DPG) family of…

A chord diagram refers to a set of chords with distinct endpoints on a circle. The intersection graph of a chord diagram $\cal C$ is defined by substituting the chords of $\cal C$ with vertices and by adding edges between two vertices…

We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…

We introduce random interlacements for transient vertex-reinforced jump processes on a general graph $G$. Using increasing finite subgraphs $G_n$ of $G$ with wired boundary conditions, we show convergence of the vertex-reinforced jump…

This paper concerns discrete-time occupancy processes on a finite graph. Our results can be formulated in two theorems, which are stated for vertex processes, but also applied to edge process (e.g., dynamic random graphs). The first theorem…