  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 well compares 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 statistics with characteristic heavy-tails:
for different topologies, an unprecedented experimental demonstration of Levy
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 ray random walk on the graph.
