Multiple citation patterns in scientific literature: The circle and hill models

The concept of tri-citation is introduced, as a logical extension of co-citation, and a geometrical model (the circle model) is devised to account for these and all other forms of multiple citation. The model is used to predict distances between documents which can be scaled metrically in two dimensional space. The model is also used to predict observed tri-citation frequencies among a set of six documents in particle physics. A further refinement of the model is suggested (the hill model) which promises to be more flexible. Implications of such spatial models for the representation of clusters of highly cited documents are discussed.