I am trying to collect a few examples of applications of line graphs in sciences other than mathematics. To be more precise: I am thinking of models where there is a clear conceptual added value in switching the paradigm from a description focused on agents (nodes) to a description focused on relations (edges).
I know: put it like this it sounds very much like I am thinking of anthropological/sociological models, and indeed they are the most natural I could come up with$^{*}$, but I do believe that similar ideas appear elsewhere, too, modulo considering graph operations/decorations that allow for more flexible descriptions.
Inter/transdisciplinary examples would be particularly appreciated.
$^{*}$ It is not by chance that line graphs were so much pushed by Frank Harary after all, of all possible graph theorists :)