  Topology identification comprises reconstructing the interaction Hamiltonian
of a quantum network by properly processing measurements of its density
operator within a fixed time interval. It finds application in several quantum
technology contexts, ranging from quantum communication to quantum computing or
sensing. In this paper, we provide analytical conditions for the solvability of
the topology identification problem for autonomous quantum dynamical networks.
The solvability condition is then converted in an algorithm for quantum network
reconstruction that is easily implementable on standard computer facilities.
The obtained algorithm is tested for Hamiltonian reconstruction on numerical
examples based on the quantum walks formalism.
