Revisited topology of Kirchoff's circuits

A novel axiomatic introduction to the topology of lumped circuits, based on a bipartite directed graph (digraph), is presented. A bipartite digraph differs from a usual digraph in that it is based on two distinct sets of nodes (junction nodes and component nodes) and a set of arcs (terminals). This approach makes it possible to treat two-terminal and multiterminal component in the same way. The Kirchhoff current and voltage laws are introduced as axioms over the bipartite digraph and, consequently, Tellegen's theorem is formulated. The topological aspects of the concept of equivalent circuit are formulated as a condensation of the bipartite digraph and the definition of a multiport as a particular multiterminal component is derived.<
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