The monograph, published by Cambridge University Press in 2005, presents a complete study of block modelling, one of the most frequently used tools in the analysis of social networks. In the monograph, the block modeling is generalized in such a way that it enables the analysis of many network structures. Direct optimization approaches to block modeling lead to block models, that optimally fit data and allow many generalizations. The authors of the book were awarded in 2007 with ''White Outstanding Book Award Mathematical Sociology Section'' by American Sociological Association.
COBISS.SI-ID: 23375709
The monograph combines the theory and applications of the analysis of social networks with the professional software (Pajek). The book presents the main structure concepts one after another together with applications in the social science. Every theoretical chapter is followed by a chapter on the applications, which explains how to analyse the network using the software Pajek. The software Pajek is developed by Vladimir Batagelj and Andrej Mrvar since 1996. In records of Amazon (Sales Rank), the book is on the top of the sale in many particular areas.
COBISS.SI-ID: 23375197
The class of I-graphs is the generalization over the class of the generalized Petersen graphs. Different properties of I-graphs, such as connectedness, girth, and whether they are bipartite or vertex-transitive are studied. The efficient test for isomorphism of I-graphs is given, and the automorphism groups of I-graphs are characterized. The configurations that arise from bipartite I-graphs are considered . Some of them can be realized in the plane as cyclic astral configurations. The authors show that the generalizations of Petersen graphs come with some unexpected symmetries.
COBISS.SI-ID: 13784153
The conjecture that a parametric polynomial curve of degree at most n can interpolate 2n given points in real plane is confirmed for n(=5 under certain natural restrictions. This conclusion also implies the optimal asymptotic approximation order. More generally, the optimal order 2n can be achieved as soon as the interpolating curve exists. For small n the well known conjecture of Hoellig and Koch on geometric interpolation is confirmed. The introduced approach confirms the approximation order and enables the study of special classes of curves in a new way.
COBISS.SI-ID: 14340953
The authors show that all combinatorial triangle-free configurations (v_3) for v(=18 are geometrically realizable. They show that there is a unique smallest astral (18_3) triangle-free configuration, and its Levi graph is the generalized Petersen graph G(18, 5). In addition, they present geometric realizations of the unique flag transitive triangle-free configuration (20_3) and the unique point transitive triangle-free configuration (21_3). With the paper the authors manage to connect their work with one of America’s leading groups on the field of combinatorial and graphical configurations.
COBISS.SI-ID: 13920601