Matrix-based pagerank control in hypergraphs for semantic text summaries

We present a novel description of random walks in a hypergraph using a labeled multidigraph. This is based on a special decomposition of the frequency matrix of relations. This decomposition enables intrinsic analysis and control of the random walker's behavior at the matrix level, incorporating memory and modifying its behavior based on additional walk restrictions. As an aspect to highlight about this new vision, we will point out that it allows the non-back-tracking restriction to be generalized, facilitating the use of this tool in multiple applications. This article includes an application in the field of linguistics for documents summarization and the extraction of significant phrases from them.