Abstract The increasing cooperation in science, which has led to larger co-authorship networks, requires the application of new methods of analysis of social networks in bibliographic co-authorship networks as well as in networks visible on the Web. In this context, a number of interesting papers on the “Erdős Number”, which gives the shortest path (geodesic distance) between an author and the well-known Hungarian mathematician Erdős in a co-authorship network, have been published recently. This paper develops new methods concerning the position of highly productive authors in the network. Thus a relationship of distribution of these authors among the clusters in the co-authorship network could be proved to be dependent upon the size of the clusters. Highly productive authors have, on average, low geodesic distances and thus shorter length of paths to all the other authors of a specialism compared to low productive authors, whereas the influencing possibility of highly productive scientists gets distributed amongst others in the development of the specialism. A theory on the stratification in science with respect to the over random similarity of scientists collaborating with one another, previously covered with other empirical methods, could also be confirmed by the application of geodesic distances. The paper proposes that the newly developed methodology may also be applied to visible networks in future studies on the Web. Further investigation is warranted into whether co-authorship and web networks have similar structures with regards to author productivity and geodesic distances.
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