In this article we continue our study of power structures. A dynamic quantitative theory, including the measurement of power or dominance structures is applied to citation networks. A curve somewhat similar to the Lorenz curve for inequality measurement is used. We calculate the D-measure, a normalized measure expressing the degree of dominance in a network. The D-measure of a citation network consisting of the ego (the original article) with n references and m received citations is obtained. When n=m the network is symmetric and the D-measure is 0.5; when the article did not yet receive a citation the D-measure is n/(n+1). When the article has no references then the D-measure is 1/(m+1). A real-world case is described and the evolution of its D-measure over time is shown. Our work is one way of describing an evolving ego-citation network in a quantitative way.

}, keywords = {Citation graphs, Network dynamics, Network properties, Power structure, Time Evolution}, doi = {10.5530/jscires.8.1.1}, author = {Yuxian Liu and Ronald Rousseau} } @article {40, title = {Basic Independence Axioms for the Publication-citation System}, journal = {Journal of Scientometric Research}, volume = {1}, year = {2012}, month = {September 2012}, pages = {22-27}, type = {Research Article}, chapter = {22}, abstract = {Following the idea of the Bouyssou-Marchant independence axiom, a basic independence axiom for an indicator is introduced. It is shown that the average number of citations nor the h-index satisfy this basic axiom. Among the indicators considered here only the number of publications and the number of citations satisfy the requirements of this axiom. Weaker forms of the basic independence axiom are considered. The number of citations of the most-cited article satisfies these weaker forms. When studying the h-index the notion of an h-critical publication is introduced.

}, keywords = {citations, Consistency, H-Index., Independence, Indicators, publications}, doi = {10.5530/jscires.2012.1.6}, author = {Ronald Rousseau and Fred Y Ye} }