Complex propagation on directed small world networks

The effect of directionality on the information propagation in a contagion model with complex propagation, i.e., that takes into account the need for simultaneous exposure to multiple activation sources, is studied. While it is known that complex propagation is blocked with increasing network randomness, here it is shown that network directionality affects such a result, leading to several different behaviors depending on the preservation of the in-degree or out-degree. The critical points for the occurrence of complex propagation in 1D directed small world networks are determined. It is shown that these points only depend on the number of outgoing links.