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We present a formulation of the determination of the impedance between anytwo nodes in an impedance network. An impedance network is described by itsLaplacian matrix L which has generally complex matrix elements. We show that bysolving the equation L u_a = lambda_a u_a^* with orthonormal vectors u_a, theeffective impedance between nodes p and q of the network is Z = Sum_a [u_{a,p}- u_{a,q}]^2/lambda_a where the summation is over all lambda_a not identicallyequal to zero and u_{a,p} is the p-th component of u_a. For networks consistingof inductances (L) and capacitances (C), the formulation leads to theoccurrence of resonances at frequencies associated with the vanishing oflambda_a. This curious result suggests the possibility of practicalapplications to resonant circuits. Our formulation is illustrated by explicitexamples.Comment: 21 pages, 3 figures; v4: typesetting corrected; v5: Eq. (63)  correcte

Theory of impedance networks: the two-point impedance andLCresonances