Where to start with social networks?
The best introduction is, in my opinion, the book by Matthew Jackson. It has a pretty nice introduction (even if you know nothing about social networks) and chapters about many of the applications of graph theory in economics.


Jackson, M. O. (2008). Social and economic networks (Vol. 3).
Princeton: Princeton University Press.


It sounds like you try to model a game on a network (i.e., using game theory with players on a network without changing the network). If this is true, then the following paper might be even more relevant:


Galeotti, A., Goyal, S., Jackson, M. O., Vega-Redondo, F., &amp; Yariv,
L. (2010). Network games. The review of economic studies, 77(1),
218-244.