How to analyze a sparse adjacency matrix?

Question

I study sparse adjacency matrices, where most cells are zeros and some of them are here and there, each relationship between two cells has a polynomial description that can be very long, and manually analyzing them takes a lot of time. My teacher offers a purely algebraic method in terms of Gröbner bases , but before continuing, I would like to learn from purely computer science and programming considerations about how to analyze sparse adjacency matrices? Are there some data mining tools to analyze them?

Answer 1

Multidimensional computation of polynomials and the Gröbner basis is an active field of research. In 1991, Sturmfels in Rare Exclusion Theory described the resulting GR methods. In the 2015 July conference , CoCoa .

SE collects awesome material on this subject, for example, → →> GR computational analysis in M2 , where you will find step-by-step examples presented in books and different answers. For sparse matrices, there are sparse matrix algorithms built with GR fundamentals, such as the Faugère F4 and F5 algorithms based on the Buchberger algorithm.

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