Related papers: k-Connectivity of Random Key Graphs
In this paper, we study the connectivity of a one-dimensional soft random geometric graph (RGG). The graph is generated by placing points at random on a bounded line segment and connecting pairs of points with a probability that depends on…
We investigate the secure connectivity of wireless sensor networks under the random key distribution scheme of Eschenauer and Gligor. Unlike recent work which was carried out under the assumption of full visibility, here we assume a…
In this paper, we investigate the secure connectivity of wireless sensor networks utilizing the heterogeneous random key predistribution scheme, where each sensor node is classified as class-$i$ with probability $\mu_i$ for $i=1,\ldots,r$…
We consider wireless sensor networks under a heterogeneous random key predistribution scheme and an on-off channel model. The heterogeneous key predistribution scheme has recently been introduced by Ya\u{g}an - as an extension to the…
We propose inhomogeneous random K-out graphs $\mathbb{H}(n; \pmb{\mu}, \pmb{K}_n)$, where each of the $n$ nodes is assigned to one of $r$ classes independently with a probability distribution $\pmb{\mu} = \{\mu_1, \ldots, \mu_r\}$. In…
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…
Random $s$-intersection graphs have recently received much interest in a wide range of application areas. Broadly speaking, a random $s$-intersection graph is constructed by first assigning each vertex a set of items in some random manner,…
This paper, based on $k$-NN graph, presents symmetric $(k,j)$-NN graph $(1 \leq j < k)$, a brand new topology which could be adopted by a series of network-based structures. We show that the $k$ nearest neighbors of a node exert disparate…
Random key graphs were introduced to study various properties of the Eschenauer-Gligor key predistribution scheme for wireless sensor networks (WSNs). Recently this class of random graphs has received much attention in contexts as diverse…
Let $d,n\in \mathbb{N}$ be such that $d=\omega(1)$, and $d\le n^{1-a}$ for some constant $a>0$. Consider a $d$-regular graph $G=(V, E)$ and the random graph process that starts with the empty graph $G(0)$ and at each step $G(i)$ is obtained…
A k-tree is either a complete graph on (k+1) vertices or given a k-tree G' with n vertices, a k-tree G with (n+1) vertices can be constructed by introducing a new vertex v and picking a k-clique Q in G' and then joining each vertex u in Q.…
In several applications in distributed systems, an important design criterion is ensuring that the network is sparse, i.e., does not contain too many edges, while achieving reliable connectivity. Sparsity ensures communication overhead…
We consider the Eschenauer-Gligor key predistribution scheme under the condition of partial visibility with i.i.d. on-off links between pairs of nodes. This situation is modeled as the intersection of two random graphs, namely a random key…
The present study was concerned with network failure problems for simple connected undirected graphs. A connected graph becomes unconnected through edge failure, under the assumptions that only edges can fail and each edge has an identical…
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 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…
Connectivity of wireless sensor networks (WSNs) is a fundamental global property expected to be maintained even though some sensor nodes are at fault. In this paper, we investigate the connectivity of random geometric graphs (RGGs) in the…
We analyze connectivity of a heterogeneous secure sensor network that uses key predistribution to protect communications between sensors. For this network on a set $\mathcal{V}_n$ of $n$ sensors, suppose there is a pool $\mathcal{P}_n$…
We find conditions for the connectivity of inhomogeneous random graphs with intermediate density. Our results generalize the classical result for G(n, p), when p = c log n/n. We draw n independent points X_i from a general distribution on a…
Bilateral agreement based random undirected graphs were introduced and analyzed by La and Kabkab in 2015. The construction of the graph with $n$ vertices in this model uses a (random) preference order on other $n-1$ vertices and each vertex…