Bridging citation and reference distributions: Part I - The referencing-structure function and its application to co-citation and co-item studies

Citations networks are a core topic of informetrics and science studies. This article proposes to bridge the cited and citing side of citation transactions by using a disaggregated form, the “referencing-structure” function (RSF). The RSF may be also seen as the “retrieval-structure” which, in a stylized co-citation or co-word model, gives the maximum retrieval that can be expected from the bibliometric characteristics of the field (retrieval and recall features are key issues in co-citation studies). The usual citation and reference distributions may be derived from aggregates or cuts respectively, of the RSF. The RSF representation also generates new points of views on the citing-cited distributions, such as the "iso-retrieval function". A rank version of RSF is also introduced. Part I is devoted to the definition and construction of the RSF, and to the general interpretation of its various aspects in the context of co-citation studies. Generalization to other co-item (co-word, hyperlinks “co-sitations”) studies is discussed briefly. We also introduce a general form a kindred to the Weibull distribution that can be used to fit cuts of the function. The forthcoming Part II will detail empirical fits, using a few experimental files.