Related papers: Connectivity threshold for Bluetooth graphs
Fiber graphs of Gr\"obner bases from contingency tables are important in statistical hypothesis testing, where one studies random walks on these graphs using the Metropolis-Hastings algorithm. The connectivity of the graphs has implications…
We introduce a natural generalization of the Erd\H{o}s-R\'enyi random graph model in which random instances of a fixed motif are added independently. The binomial random motif graph $G(H,n,p)$ is the random (multi)graph obtained by adding…
Random key graphs represent topologies of secure wireless sensor networks that apply the seminal Eschenauer-Gligor random key predistribution scheme to secure communication between sensors. These graphs have received much attention and also…
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…
Consider a network where all nodes are distributed on a unit square following a Poisson distribution with known density $\rho$ and a pair of nodes separated by an Euclidean distance $x$ are directly connected with probability…
We investigate the secure connectivity of wireless sensor networks under a heterogeneous random key predistribution scheme and a heterogeneous channel model. In particular, we study a random graph formed by the intersection of an…
Recent research has demonstrated the importance of boundary effects on the overall connection probability of wireless networks, but has largely focused on convex domains. We consider two generic scenarios of practical importance to wireless…
We study an inhomogeneous random connection model in the connectivity regime. The vertex set of the graph is a homogeneous Poisson point process $\mathcal{P}_s$ of intensity $s>0$ on the unit cube…
In this paper, we introduce a novel model for random hypergraphs based on weighted random connection models. In accordance with the standard theory for hypergraphs, this model is constructed from a bipartite graph. In our stochastic model,…
For any positive edge density $p$, a random graph in the Erd\H{o}s-Renyi $G_{n,p}$ model is connected with non-zero probability, since all edges are mutually independent. We consider random graph models in which edges that do not share…
Random intersection graphs have received much attention for nearly two decades, and currently have a wide range of applications ranging from key predistribution in wireless sensor networks to modeling social networks. In this paper, we…
Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many…
The problem of mapping human close-range proximity networks has been tackled using a variety of technical approaches. Wearable electronic devices, in particular, have proven to be particularly successful in a variety of settings relevant…
Generation of realistic topologies plays an important role in determining the accuracy and validity of simulation studies. This study presents a discussion to justify why, and how often randomly generated adjacency matrices may not not…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
In this paper, we study the entropy of a hard random geometric graph (RGG), a commonly used model for spatial networks, where the connectivity is governed by the distances between the nodes. Formally, given a connection range $r$, a hard…
We consider ad-hoc networks consisting of $n$ wireless nodes that are located on the plane. Any two given nodes are called neighbors if they are located within a certain distance (communication range) from one another. A given node can be…
We study the richness of the ensemble of graphical structures (i.e., unlabeled graphs) of the one-dimensional random geometric graph model defined by $n$ nodes randomly scattered in $[0,1]$ that connect if they are within the connection…
Asymptotic properties of random graph sequences, like occurrence of a giant component or full connectivity in Erd\H{o}s-R\'enyi graphs, are usually derived with very specific choices for defining parameters. The question arises to which…
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…