  We introduce a Green function and analogues of other related kernels for
finite and infinite networks whose edge weights are complex-valued admittances
with positive real part. We provide comparison results with the same kernels
associated with corresponding reversible Markov chains, i.e., where the edge
weights are positive. Under suitable conditions, these lead to comparison of
series of matrix powers which express those kernels. We show that the notions
of transience and recurrence extend by analytic continuation to the
complex-weighted case even when the network is infinite. Thus, a variety of
methods known for Markov chains extend to that setting.
