While conventional tomography is associated to the Radon transform in Euclidean spaces, electrical impedance tomography, or EIT, is associated to the Radon transform in the hyperbolic plane. In this dissertation, we discuss some recent work on network tomography that can be associated to a problem similar to EIT on graphs and indicate how in some sense it may be also associated to the Radon transform on trees. We develop a strategy to determine the weight w for the case of general weighted graphs. We begin by considering relatively simple regions of interest in a graph and suitable choices for the data of the w-Neumann boundary value problem to produce a linear system of equations for the values of w.