  Convexity in a network (graph) has been recently defined as a property of
each of its subgraphs to include all shortest paths between the nodes of that
subgraph. It can be measured on the scale [0, 1] with 1 being assigned to fully
convex networks. The largest convex component of a graph that emerges after the
removal of the least number of edges is called a convex skeleton. It is
basically a tree of cliques, which has been shown to have many interesting
features. In this article the notions of convexity and convex skeletons in the
context of scientific collaboration networks are discussed. More specifically,
we analyze the co-authorship networks of Slovenian researchers in computer
science, physics, sociology, mathematics, and economics and extract convex
skeletons from them. We then compare these convex skeletons with the residual
graphs (remainders) in terms of collaboration frequency distributions by
various parameters such as the publication year and type, co-authors' birth
year, status, gender, discipline, etc. We also show the top-ranked scientists
by four basic centrality measures as calculated on the original networks and
their skeletons and conclude that convex skeletons may help detect influential
scholars that are hardly identifiable in the original collaboration network. As
their inherent feature, convex skeletons retain the properties of collaboration
networks. These include high-level structural properties but also the fact that
the same authors are highlighted by centrality measures. Moreover, the most
important ties and thus the most important collaborations are retained in the
skeletons.
