Matrices of Forests and the Analysis of Digraphs

Details Matrices of Forests and the Analysis of Digraphs Matrices of Forests and the Analysis of Digraphs

2005-08-09

arxiv.org/abs/math/0508171v2

Mathematics

Combinatorics

18 pages

Scientific paper

The matrices of spanning rooted forests are studied as a tool for analysing the structure of digraphs and measuring their characteristics. The problems of revealing the basis bicomponents, measuring vertex proximity, and ranking from preference relations / sports competitions are considered. It is shown that the vertex accessibility measure based on spanning forests has a number of desirable properties. An interpretation for the normalized matrix of out-forests in terms of information dissemination is given. Keywords: Laplacian matrix, spanning forest, matrix-forest theorem, proximity measure, bicomponent, ranking, incomplete tournament, paired comparisons

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