  In this work, we present novel general analytical solutions for the currents
that are developed in the edges of network-like circuits when some nodes of the
network act as sources/sinks of DC or AC current. We assume that Ohm's law is
valid at every edge and that charge at every node is conserved (with the
exception of the source/sink nodes). The resistive, capacitive, and/or
inductive properties of the lines in the circuit define a complex network
structure with given impedances for each edge. Our solution for the currents at
each edge is derived in terms of the eigenvalues and eigenvectors of the
Laplacian matrix of the network defined from the impedances. This derivation
also allows us to compute the equivalent impedance between any two nodes of the
circuit and relate it to currents in a closed circuit which has a single
voltage generator instead of many input/output source/sink nodes. Contrary to
solving Kirchhoff's equations, our derivation allows to easily calculate the
redistribution of currents that occurs when the location of sources and sinks
changes within the network. Finally, we show that our solutions are identical
to the ones found from Circuit Theory node analysis.
