相关论文: Connectivity of Large Scale Networks: Emergence of…

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…

Connectivity is one of the most fundamental properties of wireless multi-hop networks. A network is said to be connected if there is a path between any pair of nodes. A convenient way to study the connectivity of a random network is by…

This paper provides a necessary and sufficient condition for a random network with nodes Poissonly distributed on a unit square and a pair of nodes directly connected following a generic random connection model to be asymptotically almost…

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…

Consider a graph on $n$ uniform random points in the unit square, each pair being connected by an edge with probability $p$ if the inter-point distance is at most $r$. We show that as $n\to\infty$ the probability of full connectivity is…

In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…

Let $G=G_{n,k}$ denote the graph formed by placing points in a square of area $n$ according to a Poisson process of density 1 and joining each point to its $k$ nearest neighbours. Balister, Bollob\'as, Sarkar and Walters proved that if…

Consider the random graph $G({\mathcal P}_{n},r)$ whose vertex set ${\mathcal P}_{n}$ is a Poisson point process of intensity $n$ on $(- \frac{1}{2}, \frac{1}{2}]^d$, $d \geq 2$. Any two vertices $X_i,X_j \in {\mathcal P}_{n}$ are connected…

Let S_{n,k} denote the random geometric graph obtained by placing points inside a square of area n according to a Poisson point process of intensity 1 and joining each such point to the k=k(n) points of the process nearest to it. In this…

Xue and Kumar have established that the number of neighbors required for connectivity of wireless networks with N uniformly distributed nodes must grow as log(N), and they also established that the actual number required lies between…

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…

We give an exact solution for the complete distribution of component sizes in random networks with arbitrary degree distributions. The solution tells us the probability that a randomly chosen node belongs to a component of size s, for any…

We present a method for the construction of ensembles of random networks that consist of a single connected component with a given degree distribution. This approach extends the construction toolbox of random networks beyond the…

Limiting distributions are derived for the sparse connected components that are present when a random graph on $n$ vertices has approximately $\half n$ edges. In particular, we show that such a graph consists entirely of trees, unicyclic…

We establish the Strong Poisson Hypothesis for symmetric closed networks. In particular, the asymptotic independence of the nodes -- as the size of the system tends to infinity -- is proved.

We provide arguments for the property of the degree-degree correlations of giant components formed by the percolation process on uncorrelated random networks. Using the generating functions, we derive a general expression for the…

In the infinite configuration network the links between nodes are assigned randomly with the only restriction that the degree distribution has to match a predefined function. This work presents a simple equation that gives for an arbitrary…

Consider the geometric graph on $n$ independent uniform random points in a connected compact region $A$ of ${\bf R}^d, d \geq 2$, with $C^2$ boundary, or in the unit square, with distance parameter $r_n$. Let $K_n$ be the number of…

Over the years, quantifying the similarity of nodes has been a hot topic in complex networks, yet little has been known about the distributions of node-similarity. In this paper, we consider a typical measure of node-similarity called the…

We introduce the study of \textit{randomly oriented divisor graphs}. For each $\rho \in [0,1]$, the randomly oriented divisor graph $\mathcal{D}_\rho(N)$ is obtained from the divisor graph on $\{1, 2, \ldots, N\}$ by directing each edge…