The localization of short events arising within a network subsequently leading to wave propagation into it, is of interest in many applications. This work extend [1] which demonstrated the identifiability of a source from two detectors in a N nodes graph. We show that, rather than a source, a boundary condition identification is also possible and demonstrate a generalyzed unicity result. Furthermore, we extend the identification algorithm proposed in [1] to an arbitrary number of sensors, and estimate its complexity which depends on sensors number Ns and time dicretisation Nt. Increasing detectors number increases source identification robustness to noise up to a cutoff number being a small fraction of N. This cutt-off detector density for efficiency in noise reduction is of practical significance. We also analyze and discuss the method sensitivity to total recording time Te, sampling frequency, and signal to noise ratio. Finally we propose a pre-sectorisation to improve the systematic exploration algorithm proposed in [1] and we show a O(N) drop in complexity leading to a O(N 3) cost for the source identification. Several tests of the method on model and real graphs confirm and support the presented results.