= Kirchhoff cycle law
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= Kirchhoff's second law
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= Kirchhoff's voltage law
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The <Kirchhoff cycle law> says the directed sum of <voltage> drops around every <graph cycle> is zero. For unit <edge> resistance this is the sum of signed currents around the <graph cycle>. With unit <edge> resistance, the current is a <voltage> gradient: define the <voltage> difference by summing drops along a <graph path>. The difference of the sums along two <graph paths> is a sum around closed walks; decomposing these into <graph cycles> makes it zero. Together with the <Kirchhoff node law>, the resulting <graph Laplacian> equation determines current uniquely on a finite connected network.
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