  We introduce various notions of quantum symmetry in a directed or undirected
multigraph with no isolated vertex and explore relations among them. If the
multigraph is single edged (that is, a simple graph where loops are allowed),
all our notions of quantum symmetry reduce to already existing notions of
quantum symmetry provided by Bichon and Banica. Our constructions also show
that any multigraph with at least two pairs of vertices with multiple edges
among them possesses genuine quantum symmetry.
