Cognitive photonic networks are researched to efficiently solve computationally hard problems. Flexible fabrication techniques for the implementation of such networks into compact and scalable chips are desirable for the study of new optical computing schemes and algorithm optimization. Here we demonstrate a femtosecond laser-written optical oracle based on cascaded directional couplers in glass, for the solution of the Hamiltonian path problem. By interrogating the integrated photonic chip with ultrashort laser pulses, we were able to distinguish the different paths traveled by light pulses, and thus infer the existence or the absence of the Hamiltonian path in the network by using an optical correlator. This work proves that graph theory problems may be easily implemented in integrated photonic networks, down scaling the net size and speeding up execution times.