TITLE: Applications of line graphs
QUESTION [5 upvotes]: 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 :)

REPLY [4 votes]: Consider a wireless adhoc network that can be modeled as a graph $G=(V,E)$.  Two links $e, f \in E$ cannot be simultaneously active if they are incident to the same node. This type of interference is called primary interference.  The graph that models this interference is the line graph of $G$.  More details about this application can be found in my paper (at http://link.springer.com/article/10.1007%2Fs11276-013-0680-z) and the references therein.