while learning from tutorial, I was able to understand first paragraph clearly. I can also see that we just need to find out elementary cycles in graph(which can be done with https://www.quora.com/How-can-we-find-all-simple-cycles-in-an-undirected-graph-efficiently-How-do-I-find-the-points-that-are-forming-a-cycle-in-a-graph , an answer written by Aditya Prakash) .

Now I am not able to grasp how does gaussian method works. I have also tried to look into some solutions like, born2rule , rajat1603 , shubhamgoyal__ . all this solutions look very similar, which uses gaussian method.

so , can someone help me out with gaussian method ? what it actually does ? and when can we use it ?