Modelling and measuring multilateral co-authorship in international scientific collaboration. Part I. Development of a new model using a series expansion approach

International co-operation has strongly intensified during the last decades owing to rapid developments in scientific communication. Economic, political, and intra-scientific factors also strongly influence international collaboration links among individual countries. Obviously research results of international scientific co-operation are reflected in the documented scientific communication as international co-authorship links in scientific publications. Most bibliometric studies on this issue pertain to the share of international co-authored papers in national publication output and their impact on national and international research, or to the analysis and mapping of the structure of collaboration links. The present study attempts to develop a model to measure and analyse the extent of multilateral international co-authorship links. A new indicator, the Multilateral Collaboration Index (rho) is introduced and analysed as a function of the share of internationally co-authored papers (f). Based on f a series expansion approach is applied that can be considered an extension of a fractionation model by Nederhof and Meed and allows classifying the extent of multilateral links both among science fields and among individual countries. The paper is concluded by a first attempt to estimate the errors involved in our approach.