  Multiple sinks competition is investigated for a walker diffusing on directed
complex networks. The asymmetry of the imposed spatial support makes the system
non transitive. As a consequence, it is always possible to identify a suitable
location for the second absorbing sink that screens at most the flux of agents
directed against the first trap, whose position has been preliminarily
assigned. The degree of mutual competition between pairs of nodes is
analytically quantified through apt indicators that build on the topological
characteristics of the hosting graph. Moreover, the positioning of the second
trap can be chosen so as to minimize, at the same time the probability of being
in turn shaded by a thirdly added trap. Supervised placing of absorbing traps
on a asymmetric disordered and complex graph is hence possible, as follows a
robust optimization protocol. This latter is here discussed and successfully
tested against synthetic data.
