  We introduce the characterization of a class of quantum PageRank algorithms
in a scenario in which some kind of quantum network is realizable out of the
current classical internet web, but no quantum computer is yet available. This
class represents a quantization of the PageRank protocol currently employed to
list web pages according to their importance. We have found an instance of this
class of quantum protocols that outperforms its classical counterpart and may
break the classical hierarchy of web pages depending on the topology of the
web.
