The term double cover has several distinct meanings in mathematics.
In topology and algebraic geometry, a double cover is a map 
of degree 2, meaning that the preimage of a point
consists of two points when multiplicities are counted. For a topological covering
map, every point of 
has two distinct preimages. A branched double cover
is two-to-one away from its branch locus, while points
on the branch locus have fewer than two distinct
preimages but still have total multiplicity 2.
In graph theory, a double cover of a graph 
is a graph cover 
for which every fiber 
contains two lifts
of 
(Gross and Tucker 1987). The bipartite
double graph is a standard example. This meaning is distinct from a cycle
double cover, in which a collection of cycles contains every edge of a graph
exactly twice.
