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.