Probing the h-core: an investigation of the tail-core ratio for rank distributions

The set of citations received by a set of publications consists of citations received by articles in the h-core and citations received by articles in the h-tail. Denoting the cardinalities of these fours sets as C, P, C (H) and C (T) we introduce the tail-core ratio (C (T)/C (H)) and show that in practical cases this ratio tends to increase. Introducing further the k-index, defined as k = (C/P)/(C (T)/C (H)), we show that this index decreases in most practical cases. A power law model is in accordance with these practical observations.