153 research outputs found
Tournaments and Even Graphs are Equinumerous
A graph is called \emph{odd} if there is an orientation of its edges and an
automorphism that reverses the sense of an odd number of its edges, and
\emph{even} otherwise. Pontus von Br\"omssen (n\'e Andersson) showed that the
existence of such an automorphism is independent of the orientation, and
considered the question of counting pairwise non-isomorphic even graphs. Based
on computational evidence, he made the rather surprising conjecture that the
number of pairwise non-isomorphic \emph{even graphs} on vertices is equal
to the number of pairwise non-isomorphic \emph{tournaments} on vertices. We
prove this conjecture using a counting argument with several applications of
the Cauchy-Frobenius Theorem
Social Network Analysis with sna
Modern social network analysis---the analysis of relational data arising from social systems---is a computationally intensive area of research. Here, we provide an overview of a software package which provides support for a range of network analytic functionality within the R statistical computing environment. General categories of currently supported functionality are described, and brief examples of package syntax and usage are shown.
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