  We present an algorithm for solving inverse problems on graphs analogous to
those arising in diffuse optical tomography for continuous media. In
particular, we formulate and analyze a discrete version of the inverse Born
series, proving estimates characterizing the domain of convergence,
approximation errors, and stability of our approach. We also present a
modification which allows additional information on the structure of the
potential to be incorporated, facilitating recovery for a broader class of
problems.
