Related papers: The Secrecy Graph and Some of its Properties
A novel unified Bayesian framework for network detection is developed, under which a detection algorithm is derived based on random walks on graphs. The algorithm detects threat networks using partial observations of their activity, and is…
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 consider a version of continuum long-range percolation on finite boxes of $\mathbb{R}^d$ in which the vertex set is given by the points of a Poisson point process and each pair of two vertices at distance $r$ is connected with…
We consider the Bernoulli bond percolation process (with parameter $p$) on infinite graphs and we give a general criterion for bounded degree graphs to exhibit a non-trivial percolation threshold based either on a single isoperimetric…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
Graphs and network data are ubiquitous across a wide spectrum of scientific and application domains. Often in practice, an input graph can be considered as an observed snapshot of a (potentially continuous) hidden domain or process.…
We introduce a new way to sample inhomogeneous random graphs designed to have a lot of flexibility in the assignment of the degree sequence and the individual edge probabilities while remaining tractable. To achieve this we run a Poisson…
A graph is a structure composed of a set of vertices (i.e.nodes, dots) connected to one another by a set of edges (i.e.links, lines). The concept of a graph has been around since the late 19$^\text{th}$ century, however, only in recent…
Modeling power transmission networks is an important area of research with applications such as vulnerability analysis, study of cascading failures, and location of measurement devices. Graph-theoretic approaches have been widely used to…
The random graph of Erdos and Renyi is one of the oldest and best studied models of a network, and possesses the considerable advantage of being exactly solvable for many of its average properties. However, as a model of real-world networks…
The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant…
Message passing techniques on networks encompasses a family of related methods that can be employed to ascertain many important properties of a network. It is widely considered to be the state of the art formulation for networked systems…
Consider orthogonal planes in the 3-D space representing floors and walls in a large building. These planes divide the space into rooms where a wireless infrastructure is deployed. This paper is focused on the analysis of the correlated…
The ability to control a complex network towards a desired behavior relies on our understanding of the complex nature of these social and technological networks. The existence of numerous control schemes in a network promotes us to wonder:…
Graph auto-encoders have proved to be useful in network embedding task. However, current models only consider explicit structures and fail to explore the informative latent structures cohered in networks. To address this issue, we propose a…
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…
We consider the following dynamic Boolean model introduced by van den Berg, Meester and White (1997). At time 0, let the nodes of the graph be a Poisson point process in R^d with constant intensity and let each node move independently…
Network complexity has been studied for over half a century and has found a wide range of applications. Many methods have been developed to characterize and estimate the complexity of networks. However, there has been little research with…
Complex systems of interacting components often can be modeled by a simple graph $\mathcal{G}$ that consists of a set of $n$ nodes and a set of $m$ edges. Such a graph can be represented by an adjacency matrix $A\in\R^{n\times n}$, whose…
Due to their conceptual and mathematical simplicity, Erd\"os-R\'enyi or classical random graphs remain as a fundamental paradigm to model complex interacting systems in several areas. Although condensation phenomena have been widely…