We study a supremacy distribution in evolving Barabasi-Albert networks. The
supremacy si of a node i is defined as a total number of all nodes that
are younger than i and can be connected to it by a directed path. For a
network with a characteristic parameter m=1,2,3,... the supremacy of an
individual node increases with the network age as t(1+m)/2 in an
appropriate scaling region. It follows that there is a relation s(k)∼km+1 between a node degree k and its supremacy s and the supremacy
distribution P(s) scales as s−1−2/(1+m). Analytic calculations basing on
a continuum theory of supremacy evolution and on a corresponding rate equation
have been confirmed by numerical simulations.Comment: 4 pages, 4 figure