Related papers: Zero-one laws for connectivity in inhomogeneous ra…
Hypergraphs, graph generalizations where edges are conglomerates of $r$ nodes called hyperedges of rank $r\geq 2$, are excellent models to study systems with interactions that are beyond the pairwise level. For hypergraphs, the node degree…
Social awareness and social ties are becoming increasingly popular with emerging mobile and handheld devices. Social trust degree describing the strength of the social ties has drawn lots of research interests in many fields in wireless…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…
To establish secure (point-to-point and/or broadcast) communication channels among the nodes of a wireless sensor network is a fundamental task. To this end, a plethora of (socalled) key pre-distribution schemes have been proposed in the…
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…
To achieve security in wireless networks, it is important to be able to encrypt and authenticate messages sent among sensor nodes. Due to resource constraints, achieving such key agreement in wireless sensor networks in nontrivial. Blom's…
Each graphon $W:\Omega^2\rightarrow[0,1]$ yields an inhomogeneous random graph model $G(n,W)$. We show that $G(n,W)$ is asymptotically almost surely connected if and only if (i) $W$ is a connected graphon and (ii) the measure of elements 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…
This paper presents an applicability analysis over a novel integer programming model devoted to optimize power consumption efficiency in heterogeneous wireless sensor networks. This model is based upon a schedule of sensor allocation plans…
Connectivity and coverage are two crucial problems for wireless sensor networks. Several studies have focused on proposing solutions for improving and adjusting the initial deployment of a wireless sensor network to meet these two criteria.…
We formalize the problem of detecting a community in a network into testing whether in a given (random) graph there is a subgraph that is unusually dense. We observe an undirected and unweighted graph on N nodes. Under the null hypothesis,…
In this paper we study the connectivity problem for wireless networks under the Signal to Interference plus Noise Ratio (SINR) model. Given a set of radio transmitters distributed in some area, we seek to build a directed strongly connected…
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…
The accurate and low-cost localization of sensors using a wireless sensor network is critically required in a wide range of today's applications. We propose a novel, robust maximum likelihood-type method for distributed cooperative received…
In this work we introduce Dynamic Random Geometric Graphs as a basic rough model for mobile wireless sensor networks, where communication distances are set to the known threshold for connectivity of static random geometric graphs. We…
This paper describes and analyzes a hierarchical gossip algorithm for solving the distributed average consensus problem in wireless sensor networks. The network is recursively partitioned into subnetworks. Initially, nodes at the finest…
Let the class A of graphs be bridge-addable; that is, whenever a graph G in A has vertices u and v in different components then the graph G+uv is in A. For a random graph sampled uniformly from the graphs in A on vertex set {1,..,n}, there…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
In this paper, we present a communication-free algorithm for distributed coverage of an arbitrary network by a group of mobile agents with local sensing capabilities. The network is represented as a graph, and the agents are arbitrarily…
We consider uniform random cographs (either labeled or unlabeled) of large size. Our first main result is the convergence towards a Brownian limiting object in the space of graphons. We then show that the degree of a uniform random vertex…