Abstract
We explore the “oriented line graph” construction associated with a hypergraph, leading to a construction of pairs of strongly connected directed graphs whose adjacency operators have the same spectra. We give conditions on a hypergraph so that a hypergraph and its dual give rise to isospectral, but non-isomorphic, directed graphs. The proof of isospectrality comes from an argument centered around hypergraph zeta functions as defined by Storm. To prove non-isomorphism, we establish a Whitney-type result by showing that the oriented line graphs are isomorphic if and only if the hypergraphs are.