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Matrices of forests, analysis of networks, and ranking problems

The matrices of spanning rooted forests are studied as a tool for analysing the structure of networks and measuring their properties. The problems of revealing the basic 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 stochastic matrix of out-forests in terms of information dissemination is given.

preprint2013arXivOpen access
Pavel ChebotarevRafig Agaev
math.CONetworking and Internet ArchitectureComputer VisionDiscrete Mathematics
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Pavel ChebotarevRafig Agaev

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