We consider quantum dynamics on a graph, with repeated strong measurements performed locally at a fixed time interval $\tau$. For example a particle starting on node $x$ and measurements performed on another node $x'$. From the basic postulates of quantum mechanics the string of measurements yields a sequence no,no,no, $\cdots$ and finally in the $n$-th attempt a yes, i.e. the particle is detected. Statistics of the first detection time $n \tau$ are investigated, and compared with the corresponding classical first passage problem. Dark states, Zeno physics, a quantum renewal equation, winding number for the first return problem (work of A. Grunbaum et al.), total detection probability, detection time operators and time wave functions are discussed.