  A drawing of a graph $G$ is radial if the vertices of $G$ are placed on
concentric circles $C_1, \ldots, C_k$ with common center $c$, and edges are
drawn radially: every edge intersects every circle centered at $c$ at most
once. $G$ is radial planar if it has a radial embedding, that is, a
crossing-free radial drawing. If the vertices of $G$ are ordered or partitioned
into ordered levels (as they are for leveled graphs), we require that the
assignment of vertices to circles corresponds to the given ordering or
leveling. A pair of edges $e$ and $f$ in a graph is independent if $e$ and $f$
do not share a vertex.
  We show that a graph $G$ is radial planar if $G$ has a radial drawing in
which every two independent edges cross an even number of times; the radial
embedding has the same leveling as the radial drawing. In other words, we
establish the strong Hanani-Tutte theorem for radial planarity. This
characterization yields a very simple algorithm for radial planarity testing.
