Comments on “A Hirsch-type index of co-author partnership ability”

Abstract

In a recent contribution to this journal Andras Schubert proposed the partnership ability index, denoted as u (Schubert 2012). He pointed out that his idea fits into the framework introduced in (Zhao et al. 2011). Indeed, Zhao et al. defined the h-degree of node n in a weighted network as the number dh(n) if dh(n) is the largest natural number such that n has at least dh(n) links each with strength at least equal to dh(n). In this context weights are assumed to be natural numbers. Applying this definition to a partnership, e.g., a coauthorship, network, this number becomes the largest natural number P such that an actor has at least P partners with whom he/she had at least P joint actions. Replacing P with u gives exactly Schubert’s partnership ability index. This shows that u is a special case of the h-degree. The application of u to co-authorship networks, movie actor networks and sexual encounter networks can all be considered as special cases of the h-degree. Schubert (2012) notes that u is equal to one if—in a co-authorship network—the author has an arbitrary number of double-authored papers with the same co-author; or if the author has an arbitrary number of co-authored papers with no co-author occurring more than once. Yet, there is a third case, namely when the author has an arbitrary number of doubleauthored papers with the same co-author and an arbitrary number of co-authored papers with other authors such that no co-author occurs more than once. I would like to take this opportunity to correct a mistake in (Zhao et al. 2011). In Table 1 the w-lobby index of node C is 2 and not 3 as printed. In conclusion I would like to say that, as suggested by Schubert, the partnership ability index and its generalizations have a lot of potential not only in the field of informetrics, but certainly also in sociological studies.