We propose a procedure to generate dynamical networks with bursty, possibly repetitive and correlated temporal behaviors. Regarding any weighted directed graph as being composed of the accumulation of paths between its nodes, our construction uses random walks of variable length to produce time-extended structures with adjustable features. The procedure is first described in a general framework. It is then illustrated in a case study inspired by a transportation system for which the resulting synthetic network is shown to accurately mimic the empirical phenomenology.