Are there any textbooks or articles that formalizes/models electrical circuits (e.g. using graphs, which is probably the most likely approach to be taken) in a precise manner such that we could rigorously prove properties about circuits, like series and parallel sub-circuit substitutions, delta-wye conversions, Thevenin/Norton's theorems, the fact that every circuit has a unique solution for each voltage/current (given that initial conditions are properly set for circuits whose equations are differential), and so on?
I think I can sketch some of the proofs but it would really help if there were any references written by experts.