In his proof of the Shannon capacity of a graph, Lovasz utilizes a coordinate representation of the pentagon (namely an orthonormal representation). Who first utilized a coordinate representation for finite/infinite graphs for any purpose? I am thinking a general vector valued representation. And not just a $2$-d representation or a 'fixed' dimensional representation. 



Who first used/gave a coordinate representation of a graph?
If by "coordinate representation" you mean the assignment of geometric positions to a graph that was initially given as a purely combinatorial structure, then one possible contender is the proof of [Steinitz's theorem](https://en.wikipedia.org/wiki/Steinitz's_theorem) by


Steinitz, E. (1922), "Polyeder und Raumeinteilungen", *Encyclopädie der mathematischen Wissenschaften*, Band 3 (Geometries), pp. 1–139.


Somewhat later we have the proof of [Fáry's theorem](https://en.wikipedia.org/wiki/F%C3%A1ry's_theorem) by


Wagner, Klaus (1936), "Bemerkungen zum Vierfarbenproblem", *Jahresbericht der Deutschen Mathematiker-Vereinigung* 46: 26–32.


(Fáry's and Stein's independent discoveries were later) and the drawings of [sociograms](https://en.wikipedia.org/wiki/Sociogram) in


Moreno, J. L. (1934), Who Shall Survive?, New York, N.Y.: Beacon House.


