## Günter Rote:

# Characterization of the response maps of alternating-current networks

Manuscript, April 2019, 6 pages, arXiv:1904.02031 [math.CO], submitted for
publication.
→BibTeX
### Abstract

An *alternating-current network* is an undirected graph in which
each edge is weighted by a *conductance*, a complex number with
positive real part. Some nodes are designated as *boundary nodes*. The
*response map* is the linear map from the vector of *voltages* at the
boundary nodes to the vector of *currents* flowing into the network through
these nodes.

We prove that the known necessary conditions for a linear map to be a
response map are
sufficient, and we show how to construct an appropriate alternating-current
network for a given response map.

Last update: April 4, 2019.