Complex optical networks containing one or more gain sections are investigated, and the evidence of lasing action is reported; the emission spectrum reflects the topological disorder induced by the connections. A theoretical description compares well with the measurements, mapping the networks to directed graphs and showing the analogies with the problem of quantum chaos on graphs. We show that the interplay of chaotic diffusion and amplification leads to an emission statistic with characteristic heavy tails: for different topologies, an unprecedented experimental demonstration of Lévy statistics expected for random lasers is here provided for a continuous-wave pumped system. This result is also supported by a Monte Carlo simulation based on the ray random walk on the graph.