A Survey of Proximity Graphs in Wireless Networks

Abstract

Network topology can be represented by the proximity graph defined as a graph with a set of vertices V and a set of edges E such that a directed edge (u,v) belong to E if and only if the point v is in the neighborhood induced by some predefined proximity measures of point u. This paper reviews some important graphs obtained so far, and the contents mainly concentrated in five aspects of those proximity graphs including their definitions or conceptions, construction algorithms, illustrations, topological relationships, and some parameters. This paper also outlines several further research directions.

Optimal Topology of Multilayer Urban Traffic Networks

“…ese graphs are related as MST ⊆ RNG ⊆ GG [61]; generally, the RNG can be created easily using a distributed algorithm, but the accessibility and connectivity are 4 Complexity relatively poorer than those of GG [61,63]. Referring to Ding et al [25], we can see that the RNG and GG can be used to represent connected rail networks and road networks.…”

“…is the intersection of the circular region of points p and q, with the radius being the distance between points p and q as δ(p, q). If there does not exist such a point g in A p,q (q ≠ g), point q is called a "relative neighbor" of point p. e RNG is widely used in wireless networks, circuits, navigation, and location [61].…”