Mutual Coupling
In conventional graph representation of circuits, there is no means of explicitly representing mutual inductive couplings, such as occurs in a transformer, and such components may result in a disconnected graph with more than one separate part. For convenience of analysis, a graph with multiple parts can be combined into a single graph by unifying one node in each part into a single node. This makes no difference to the theoretical behaviour of the circuit so analysis carried out on it is still valid. It would, however, make a practical difference if a circuit were to be implemented this way in that it would destroy the isolation between the parts. An example would be a transformer earthed on both the primary and secondary side. The transformer still functions as a transformer with the same voltage ratio but can now no longer be used as an isolation transformer.
More recent techniques in graph theory are able to deal with active components, which are also problematic in conventional theory. These new techniques are also able to deal with mutual couplings.
Read more about this topic: Topology (electrical Circuits), Graph Theory
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