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Starting from topological principles we first recall the elementary onesgiving Kirchhoff's laws for current conservation. Using in a second step theproperties of spaning tree, we show that currents are under one hypothesisintrinsically boundaries of surfaces flux. Naturally flux appears as the objectfrom which the edge comes from. The current becomes the magnetomotive force(mmf) that creates the flux in the magnetostatic representation. Using a metricand an Hodge's operator, this flux creates an electromotive force (emf). Thisemf is finally linked with the current to give the fundamental tensor - or"metric" - of the Kron's tensorial analysis of networks. As it results in alink between currents of cycles (surface boundaries) and energy sources in thenetwork, we propose to symbolize this cross talk using chords between cycles inthe graph structure on which the topology is based. Starting then from energiesrelations we show that this metric is the Lagrange's operator of the circuit.But introducing moment space, the previous results can be extended to non localinteractions as far field one. And to conclude, we use the same principle tocreate general relation of information exchange between networks as functorsbetween categories.

Kron's method and cell complexes for magnetomotive and electromotive forces