In invisible colleges the relative frequency of coauthorships is higher between scientists with the same number of publications than between authors of different ones. The opposite is valid in institutionalized communities.
This study deals with the uniformity of the collaboration process within the scientist's system by describing all two-dimensional
and three-dimensional referential patterns with only one nonliear function. The variety of these patterns is expressed in
dependence upon the conditions or environment that induced them by means of varying the parameters of this non-linear function.
Based on their similarity these various patterns can be divided into different types.
A complex structure measure for social groups was established with a view to reflecting the degree of interaction within a social group. The quantitative degrees of relationship between two group members each and their distributions within the group are considered. These distributions can be characterized quantitatively on different hierarchical levels to which a specific meaning can be attributed. The complex structure measure is a combination of measures for the different hierarchical levels. A stratification of scientists based on the number of publications in a journal is reflected in the results obtained by the complex structure measure. Specific information is provided both by the complex structure measure and by the measure on different levels.
The supposition for Pinski's measures of research interactivity is a size reduced form of a citation matrix, which makes it possible to compare journals of different sizes. A futher development of the measures of research interactivity can be achieved by using a complex structure measure. In addition to the relative scope of citations, which is taken into consideration by Pinski's measures, the distributions of these values on the elements of the matrix are involved in calculating new measures of interactivity whose content is different from that of Pinski's measures.
A research group is considered to be a system and the scientists the elements in this system. The degree of interaction among scientists is determined by means of a complex structure measure for groups. It is shown that optimum cooperation structures depend on group size. In addition, it was possible to determine an optimum group size. Various hypotheses have been verified employing the same data material by using several levels of the structure measure.
A theoretical approach was developed to raising the effectivenes of research groups as adaptable systems. If performance is the aim of the research group, adaptation to the changing conditions in the research process has to be one of its essential principles underlying its development. Empirically it was shown that several independent components of the cooperation structure that were simultaneously adapted to different changing conditions exerted a strong influence on performance. There is the hypothesis that the principle of adaptation of cooperation structure can be generally extended to the adaptation of other group characteristics.
The characteristic structure underlying interpersonal relations in social networks in general is identifiable in a great number
of such social processes, as the spread of diseases, the propagation of information, the change of views or the dissemination
of technological innovations. The patterns of behaviour reflected in the coauthorship networks of the invisible colleges of
physics, resemble the general structure of relations identified in social networks beyond the communities of scholars. The
patterns of behaviour are portrayed both as two-dimensional and three-dimensional models.
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.