  Let $(X,\mathbf{d})$ be a metric space, $V\subseteq X$ a finite set, and $E
\subseteq V \times V$. We call the graph $G(E,V)$ a {\em metric} graph if each
edge $(u,v) \in E$ has weight $d(u,v)$. In particular edge $(u,u)$ is in the
graph and have distance $0$. We call $G$ a {\em proximal navigation graph} or
$PN$-graph if for each edge $(u,v) \in E$ either $u=v$ or there is a node $u_1$
such that $(u,u_1) \in E$ and $\mathbf{d}(u,v) > \mathbf{d}(u_1,v)$. In such
graph it is possible to navigate greedily from an arbitrary source node to an
arbitrary target node by reducing the distance between the current node and the
target node in each step. The complete graph, the Delaunay triangulation and
the Half Space Proximal (HSP) graph (defined below in the paper) are examples
of $PN$-graphs.
  In this paper we study the relationship between $PN$-graphs and $t$-spanners
and prove that there are $PN$-graphs that are not $t$-spanners for any $t$. On
the positive side we give sufficient conditions for a $PN$-graph to be a
$t$-spanner and prove that any $PN$-graph over $\mathbb{R}^n$ under the
euclidean distance is a $t$-spanner.
