The paper presents a methodology for identifying the topology of strictly causal dynamical networks. Using a graph-theoretic representation of interconnected dynamical systems, each node is assumed to be a stochastic process whose output is influenced by an independent stochastic noise and outputs of other nodes. The links, which represent the influence of other nodes, are assumed to be strictly causal dynamical filters. When an invasive number of measured data is available, reconstruction techniques based on Granger causality are capable of tackling this problem, however, for very large networks they are rendered impractical. Under the assumption of the sparsity of a complex network including feedback and self-loops, we propose a consistent algorithm based on cycling least-squares that unveils the topology without any a priori knowledge about the structure. For non-invasive measurements, we cast the problem as a structured sparse signal recovery and propose another data-driven algorithm based on ideas borrowed from compressive sensing and matching pursuit to identify the network. To show the superiority of this method we compare its performance with those of the Granger causality and other state-of-the-art techniques through Monte-Carlo simulations.