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This article examines the inverse problem for a lossy quantum graph that isinternally excited and sensed. In particular, we supply an algorithmicmethodology for deducing the topology and geometric structure of the underlyingmetric graph. Our algorithms rely on narrowband and visibility measurements,and are therefore of considerable value to urban remote sensing applications.In contrast to the traditional methods in quantum graphs, we employ ideasrelated to algebraic and differential topology directly to our problem. Thisneatly exposes and separates the impact of the graph topology and geometry.

Inverse problems in geometric graphs using internal measurements