  By mapping the most advanced elements of the contemporary social
interactions, the world scientific collaboration network develops an extremely
involved and heterogeneous organization. Selected characteristics of this
heterogeneity are studied here and identified by focusing on the scientific
collaboration community of H. Eugene Stanley - one of the most prolific world
scholars at the present time. Based on the Web of Science records as of March
28, 2016, several variants of networks are constructed. It is found that the
Stanley #1 network - this in analogy to the Erd\H{o}s # - develops a largely
consistent hierarchical organization and Stanley himself obeys rules of the
same hierarchy. However, this is seen exclusively in the weighted network
representation. When such a weighted network is evolving, an existing relevant
model indicates that the spread of weight gets stimulation to the
multiplicative bursts over the neighbouring nodes, which leads to a balanced
growth of interconnections among them. While not exclusive to Stanley, such a
behaviour is not a rule, however. Networks of other outstanding scholars
studied here more often develop a star-like form and the central hubs
constitute the outliers. This study is complemented by a spectral analysis of
the normalised Laplacian matrices derived from the weighted variants of the
corresponding networks and, among others, it points to the efficiency of such a
procedure for identifying the component communities and relations among them in
the complex weighted networks.
