  In this paper, we introduce a variation of the well-studied Yao graphs. Given
a set of points $S\subset \mathbb{R}^2$ and an angle $0 < \theta \leq 2\pi$, we
define the continuous Yao graph $cY(\theta)$ with vertex set $S$ and angle
$\theta$ as follows. For each $p,q\in S$, we add an edge from $p$ to $q$ in
$cY(\theta)$ if there exists a cone with apex $p$ and aperture $\theta$ such
that $q$ is the closest point to $p$ inside this cone.
  We study the spanning ratio of $cY(\theta)$ for different values of $\theta$.
Using a new algebraic technique, we show that $cY(\theta)$ is a spanner when
$\theta \leq 2\pi /3$. We believe that this technique may be of independent
interest. We also show that $cY(\pi)$ is not a spanner, and that $cY(\theta)$
may be disconnected for $\theta > \pi$.
