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 subdimensional 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 nonbipartite, 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.