In network tomography, we seek to infer link status parameters (such as delay) inside a network through end-toend probe sending between (external) boundary nodes. The main challenge here is to estimate link-level attributes from end-to-end measurements. In this paper by using the idea of combinatorial compressed sensing, we provide conditions on network routing matrix under which it is possible to estimate links delay from end-to-end delay measurements. We also provide an upper-bound on the estimation error. Moreover, for a given network, we show how to design its routing matrix to achieve the minimum number of probes needed to be sent in order to estimate delay of the links inside the network.