  We view the determinant and permanent as functions on directed weighted
graphs and introduce their analogues for the undirected graphs. We prove that
the task of computing the undirected determinants as well as permanents for
planar graphs, whose vertices have degree at most 4, is \#P-complete. In the
case of planar graphs whose vertices have degree at most 3, the computation of
the undirected determinant remains \#P-complete while the permanent can be
reduced to the FKT algorithm, and therefore is polynomial.
  The undirected permanent is a Holant problem and its complexity can be
deduced from the existing literature. The concept of the undirected determinant
is new. Its introduction is motivated by the formal resemblance to the directed
determinant, a property that may inspire generalizations of some of the many
algorithms which compute the latter.
  For a sizable class of planar 3-regular graphs, we are able to compute the
undirected determinant in polynomial time.
