Graph Theory. How to find the largest independent set using Malgrange's algorithm?

Question

Algorithms

I am attaching a graph for which you need to write an algorithm in any OOP language.
I've been breaking my head for a week, and I can't figure out how to implement it....
There are two classes with a vertex and an edge, and when approaching the algorithm itself, it's just a stupor...

Answer 1

If in a week you have not realized that the graph in the figure is not an orthograph (or that all its arcs are bidirectional) - give up this hopeless task.