Related papers: Random Variables in Graph W*-Probability Spaces
We offer a new perspective on risk aggregation with FGM copulas. Along the way, we discover new results and revisit existing ones, providing simpler formulas than one can find in the existing literature. This paper builds on two novel…
In this note we extend the construction of a $C^*$-algebra associated to a self-similar graph to the case of arbitrary countable graphs. We reduce the problem to the row-finite case with no sources, by using a desingularization process.…
Random directed graphs $D(n,p)$ undergo a phase transition around the point $p = 1/n$, and the width of the transition window has been known since the works of Luczak and Seierstad. They have established that as $n \to \infty$ when $p = (1…
Over 50 years ago, Erd\H{o}s and Gallai conjectured that the edges of every graph on $n$ vertices can be decomposed into $O(n)$ cycles and edges. Among other results, Conlon, Fox and Sudakov recently proved that this holds for the random…
Many network datasets exhibit connectivity with variance by resolution and large-scale organization that coexists with localized departures. When vertices have observed ordering or embedding, such as geography in spatial and village…
Consider an n by n matrix x_ij, and consider the quantity || x_{i,pi(i)} ||_X where X is a symmetric sequence space as a random variable where the permutation pi is chosen randomly. This was considered by Kwapien and Schutt, and we extend…
We show that a number of conditions on oriented graphs, all of which are satisfied with high probability by randomly oriented graphs, are equivalent. These equivalences are similar to those given by Chung, Graham and Wilson in the case of…
Graphs and networks are common ways of depicting biological information. In biology, many different biological processes are represented by graphs, such as regulatory networks, metabolic pathways and protein--protein interaction networks.…
The exponential family of random graphs represents an important and challenging class of network models. Despite their flexibility, conventionally used exponential random graphs have one shortcoming. They cannot directly model weighted…
We study three mixing properties of a graph: large algebraic connectivity, large Cheeger constant (isoperimetric number) and large spectral gap from 1 for the second largest eigenvalue of the transition probability matrix of the random walk…
This paper develops a theory of graph classification under domain shift through a random-graph generative lens, where we consider intra-class graphs sharing the same random graph model (RGM) and the domain shift induced by changes in RGM…
Let $G$ be a dense graph with good expansion properties and not too close to being bipartite. Let $\boldsymbol d$ be a graphical degree sequence. Under very weak conditions, we find the number of subgraphs of $G$ with degree sequence…
A graph drawing in the plane is called an almost embedding if images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. We introduce integer invariants of almost embeddings: winding number, cyclic and triodic Wu…
Singular-value statistics (SVS) has been recently presented as a random matrix theory tool able to properly characterize non-Hermitian random matrix ensembles [PRX Quantum {\bf 4}, 040312 (2023)]. Here, we perform a numerical study of the…
In this work we study the dynamics of systems composed of numerous interacting elements interconnected through a random weighted directed graph, such as models of random neural networks. We develop an original theoretical approach based on…
We introduce a new `geometric realization' of an (abstract) simplicial complex, inspired by probability theory. This space (and its completion) is a metric space, which has the right (weak) homotopy type, and which can be compared with the…
In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…
A circulant graph H is defined on the set of vertices V=\left\{ 1,\ldots,n\right\} and edges E=\left\{ \left(i,j\right):\left|i-j\right|\equiv s\left(\textrm{mod}n\right),s\in S\right\} , where S\subseteq\left\{…
We improve the estimates of the subgraph probabilities in a random regular graph. Using the improved results, we further improve the limiting distribution of the number of triangles in random regular graphs.
A natural representation of random graphs is the random measure. The collection of product random measures, their transformations, and non-negative test functions forms a general representation of the collection of non-negative weighted…