Related papers: Further Properties of Random Threshold Graphs
In this paper, we investigate the spectral properties of Andr\'asfai graphs, focusing on key parameters: the second-largest and smallest eigenvalues, the number of distinct eigenvalues, and the multiplicities of the eigenvalues 1 and -1.…
A metric probability space $M$ admits thresholds if the random geometric graph on $M$ has a threshold for every monotone graph property. We connect the existence of thresholds to the uniform expansion of $M$ and prove that all standard…
Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…
We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…
We explore how the asymptotic structure of a random permutation of $[n]$ with $m$ inversions evolves, as $m$ increases, establishing thresholds for the appearance and disappearance of any classical, consecutive or vincular pattern. The…
One of the major themes of random matrix theory is that many asymptotic properties of traditionally studied distributions of random matrices are universal. We probe the edges of universality by studying the spectral properties of random…
The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and…
We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an a.s. asymptotic degree distribution, with streched exponential decay; more…
We equip the edges of a deterministic graph $H$ with independent but not necessarily identically distributed weights and study a generalized version of matchings (i.e. a set of vertex disjoint edges) in $H$ satisfying the property that…
The edge-degeneracy model is an exponential random graph model that uses the graph degeneracy, a measure of the graph's connection density, and number of edges in a graph as its sufficient statistics. We show this model is relatively…
The study of substructures in random objects has a long history, beginning with Erd\H{o}s and R\'enyi's work on subgraphs of random graphs. We study the existence of certain substructures in random subsets of vector spaces over finite…
We review results on linearly edge-reinforced random walks. On finite graphs, the process has the same distribution as a mixture of reversible Markov chains. This has applications in Bayesian statistics and it has been used in studying the…
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…
Conventionally used exponential random graphs cannot directly model weighted networks as the underlying probability space consists of simple graphs only. Since many substantively important networks are weighted, this limitation is…
We study properties of random subcomplexes of partitions returned by (a suitable form of) the Strong Hypergraph Regularity Lemma, which we call regular slices. We argue that these subcomplexes capture many important structural properties of…
We study properties of Graph Convolutional Networks (GCNs) by analyzing their behavior on standard models of random graphs, where nodes are represented by random latent variables and edges are drawn according to a similarity kernel. This…
We study some properties of graphs (or, rather, graph sequences) defined by demanding that the number of subgraphs of a given type, with vertices in subsets of given sizes, approximatively equals the number expected in a random graph. It…
Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world…
We investigate flows on graphs whose links have random capacities. For binary trees we derive the probability distribution for the maximal flow from the root to a leaf, and show that for infinite trees it vanishes beyond a certain threshold…