  Network growth is currently explained through mechanisms that rely on node
prestige measures, such as degree or fitness. In many real networks those who
create and connect nodes do not know the prestige values of existing nodes, but
only their ranking by prestige. We propose a criterion of network growth that
explicitly relies on the ranking of the nodes according to any prestige
measure, be it topological or not. The resulting network has a scale-free
degree distribution when the probability to link a target node is any power law
function of its rank, even when one has only partial information of node ranks.
Our criterion may explain the frequency and robustness of scale-free degree
distributions in real networks, as illustrated by the special case of the Web
graph.
