Percolation, connectivity, coverage and colouring of random geometric graphs
نویسندگان
چکیده
In this review paper, we shall discuss some recent results concerning several models of random geometric graphs, including the Gilbert disc model Gr , the k-nearest neighbour model G nn k and the Voronoi model GP . Many of the results concern finite versions of these models. In passing, we shall mention some of the applications to engineering and biology.
منابع مشابه
Stochastic Geometry for Wireless Networks
Covering point process theory, random geometric graphs, and coverage processes, this rigorous introduction to stochastic geometry will enable you to obtain powerful, general estimates and bounds of wireless network performance, and make good design choices for future wireless architectures and protocols that efficiently manage interference effects. Practical engineering applications are integra...
متن کاملCombinatorial and Numerical Analysis of Geographical Threshold Graphs
We analyze the structure of random graphs generated by the geographic threshold model. The model is a generalization of random geometric graphs. Nodes are distributed in space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. We show how the degree distribution, percolation and connectivity transitions, diamet...
متن کاملPercolation and Connectivity in AB Random Geometric Graphs
Given two independent Poisson point processes Φ(1),Φ(2) in Rd, the AB Poisson Boolean model is the graph with points of Φ(1) as vertices and with edges between any pair of points for which the intersection of balls of radius 2r centred at these points contains at least one point of Φ(2). This is a generalization of the AB percolation model on discrete lattices. We show the existence of percolat...
متن کاملConnectivity of Random Geometric Graphs Related to Minimal Spanning Forests
The a.s. connectivity of the Euclidean minimal spanning forest MSF(X) on a homogeneous Poisson point process X ⊂ R is an open problem for dimension d > 2. We introduce a descending family of graphs (Gn)n≥2 that can be seen as approximations to the MSF in the sense that MSF(X) = ⋂∞ n=2Gn(X). For n = 2 one recovers the relative neighborhood graph or, in other words, the β-skeleton with β = 2. We ...
متن کاملSome topological indices of graphs and some inequalities
Let G be a graph. In this paper, we study the eccentric connectivity index, the new version of the second Zagreb index and the forth geometric–arithmetic index.. The basic properties of these novel graph descriptors and some inequalities for them are established.
متن کامل