Related papers: Connectivity of Large Wireless Networks under A Ge…
We study graphs that are formed by independently-positioned needles (i.e., line segments) in the unit square. To mathematically characterize the graph structure, we derive the probability that two line segments intersect and determine…
Statistical inference using pairwise comparison data is an effective approach to analyzing large-scale sparse networks. In this paper, we propose a general framework to model the mutual interactions in a network, which enjoys ample…
There has been much recent interest in random graphs sampled uniformly from the n-vertex graphs in a suitable minor-closed class, such as the class of all planar graphs. Here we use combinatorial and probabilistic methods to investigate a…
We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely…
This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. We are interested in graph-theoretic conditions…
In this study, the concept of small worlds is investigated in the context of large-scale wireless ad hoc and sensor networks. Wireless networks are spatial graphs that are usually much more clustered than random networks and have much…
Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical…
It is becoming increasingly common to see large collections of network data objects -- that is, data sets in which a network is viewed as a fundamental unit of observation. As a result, there is a pressing need to develop network-based…
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…
Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…
The paper deals with a random connection model, a random graph whose vertices are given by a homogeneous Poisson point process on $\mathbb{R}^d$, and edges are independently drawn with probability depending on the locations of the two end…
In this paper we study the one dimensional random geometric graph when the location of the nodes are independent and exponentially distributed. We derive exact results and the limit theorems for the connectivity and other properties…
Consider a 2-dimensional soft random geometric graph $G(\lambda,s,\phi)$, obtained by placing a Poisson($\lambda s^2$) number of vertices uniformly at random in a square of side $s$, with edges placed between each pair $x,y$ of vertices…
We consider one-hop communication in wireless networks with random connections. In the random connection model, the channel powers between different nodes are drawn from a common distribution in an i.i.d. manner. An scheme achieving the…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
k-connectivity is an important measure of network robustness and resilience to random faults and disruptions. We undertake both local and global approaches to k-connectivity and calculate closed form analytic formulas for the probability…
This Letter introduces a generalization of known duplication-divergence models for growing random graphs. This general duplication-divergence model includes a new coupled divergence asymmetry rate, which allows to obtain the structure of…
Network Models with couplings between link pairs are the simplest models for a class of networks with Higher Order interactions. In this paper we give an analytic, general solution to this family of Random Graph Models extending previous…
Many real world graphs have edges correlated to the distance between them, but, in an inhomogeneous manner. While the Chung-Lu model and the geometric random graph models both are elegant in their simplicity, they are insufficient to…
Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…