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, CH and CT we introduce the tail-core ratio (CT/CH) and show that in practical cases this ratio tends to increase. Introducing further the k-index, defined as k = (C/P)/(CT/CH), we show that this index decreases in most practical cases. A power law model is in accordance with these practical observations.