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