In this paper we explore some implications of viewing graphs asgeometric objects. This approach offers a new perspective on a number of graph-theoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that respect themetric of the (possibly weighted) graph. Given a graphG we map its vertices to a normed space in an attempt to (i) keep down the dimension of the host space, and (ii) guarantee a smalldistortion, i.e., make sure that distances between vertices inG closely match the distances between their geometric images.
['Nathan Linial', 'Eran London', 'Yuri Rabinovich']
The geometry of graphs and some of its algorithmic applications