  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
