Related papers: Connectivity of Soft Random Geometric Graphs Over …
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…
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…
The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and…
In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad-hoc networks "soft" or "probabilistic"…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
We consider soft random geometric graphs, constructed by distributing points (nodes) randomly according to a Poisson Point Process, and forming links between pairs of nodes with a probability that depends on their mutual distance, the…
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…
The fault tolerance of random graphs with unbounded degrees with respect to connectivity is investigated, which relates to the reliability of wireless sensor networks with unreliable relay nodes. The model evaluates the network breakdown…
Graph-theoretic methods have seen wide use throughout the literature on multi-agent control and optimization. When communications are intermittent and unpredictable, such networks have been modeled using random communication graphs. When…
A temporal random geometric graph is a random geometric graph in which all edges are endowed with a uniformly random time-stamp, representing the time of interaction between vertices. In such graphs, paths with increasing time stamps…
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…
Soft Random Geometric Graphs (SRGGs) have been widely applied to various models including those of wireless sensor, communication, social and neural networks. SRGGs are constructed by randomly placing nodes in some space and making pairwise…
Graph-theoretic tools and techniques have seen wide use in the multi-agent systems literature, and the unpredictable nature of some multi-agent communications has been successfully modeled using random communication graphs. Across both…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
In a wide range of complex networks, the links between the nodes are temporal and may sporadically appear and disappear. This temporality is fundamental to analyze the formation of paths within such networks. Moreover, the presence of the…
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…
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…
Random geometric networks consist of 1) a set of nodes embedded randomly in a bounded domain $\mathcal{V} \subseteq \mathbb{R}^d$ and 2) links formed probabilistically according to a function of mutual Euclidean separation. We quantify how…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
Network connectivity is usually addressed for convex domains where a direct line of sight exists between any two transmitting/receiving nodes. Here, we develop a general theory for the network connectivity properties across a small opening,…