2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102163The 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 comparisons18 pagesCombinatoricsComputer Vision and Pattern RecognitionNetworking and Internet Architecture05C50; 05C05; 15A51text