  Competition among exchange interactions is able to induce novel spin
correlations on a bipartite lattice without geometrical frustration. A
prototype example is the spiral spin liquid, which is a correlated paramagnetic
state characterized by sub-dimensional degenerate propagation vectors. Here,
using spectral graph theory, we show that spiral spin liquids on a bipartite
lattice can be approximated by a further-neighbor model on the corresponding
line-graph lattice that is non-bipartite, thus broadening the space of
candidate materials that may support the spiral spin liquid phases. As
illustrations, we examine neutron scattering experiments performed on two
spinel compounds, ZnCr$_2$Se$_4$ and CuInCr$_4$Se$_8$, to demonstrate the
feasibility of this new approach and expose its possible limitations in
experimental realizations.
