What exactly are eletrical circuits as mathematical objects?

It seems quite intuitive to me, that they are geometric realization of some graph with some additional structure.

Another thing I notice is that application of KVL and KCL together turns this graph to a system of linear equations.

$$\text{circuit} \to^{KVL}_{KCL} \to \text{linear eqtns}$$

All sites I look online eg: Wiki give me undetailed answers.