Matrices of Forests and the Analysis of Digraphs
Pavel Chebotarev, Rafig Agaev

TL;DR
This paper explores matrices derived from spanning rooted forests to analyze digraph structures, revealing properties like vertex proximity and ranking, with applications in information dissemination and preference analysis.
Contribution
It introduces a novel approach using spanning forest matrices for digraph analysis, including new measures of vertex accessibility and interpretations for information flow.
Findings
Vertex accessibility measure has desirable properties
Normalized out-forest matrix interprets information dissemination
Method effectively reveals bicomponents and rankings
Abstract
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
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsTopological and Geometric Data Analysis · Graph theory and applications · Complex Network Analysis Techniques
