Abstract
We study a supremacy distribution in evolving Barabasi-Albert networks. The supremacy of a node is defined as the total number of all nodes that are not older than and can be linked to it by a directed path (including the node ). The nodes form a basin connected to the node as its in-component. For a network with a characteristic parameter , the supremacy of an individual node increases with the network age as in an appropriate scaling region. It follows that there is a relation between a node degree and its supremacy , and the supremacy distribution scales as . Analytic calculations basing on a continuum theory of supremacy evolution and on a corresponding rate equation have been confirmed by numerical simulations.
- Received 27 August 2003
DOI:https://doi.org/10.1103/PhysRevE.70.046119
©2004 American Physical Society