How to analyse a sparse adjacency matrix?

Question

I am researching sparse adjacency matrices where most cells are zeros and some ones here-and-there, each relationship between two cells has a polynomial description that can be very long and their analysis manually time-consuming. My instructor is suggesting purely algebraic method in terms of Gröbner bases but before proceeding I would like to know from purely computer science and programming perspective about how to analyse sparse adjacency matrices? Does there exist some data mining tools to analyse them?

Answer 1

Multivariate polynomial computation and Gröbner basis is an active research area. In 1991, Sturmfels in Sparse elimination theory outlined the resultant methods and GR methods. In 2015 July conference, CoCoa analysis.

SE is gathering awesome material on this such as GR computational analysis in M2 where you an find step-by-step examples outlined in the books and different answers. For sparse matrices, there are sparse matrix algorithms built with GR bases such as Faugère's F4 and F5 algorithms that is based on Buchberger algorithm.

Updating this when finding more!