How can i make a complex analysis for Prim's Algorithm

Working on Prim's algorithm you need to do two things:

1. Implement it in pseudo-code or actual code (say Python for example). You can pick but any approachneeds to have lots of details and comments. I am happy to help as well with this.
2. Analyze the algorithm. You can look at complexity or proof that it works here. You can choose. If you go with complexity, you will be looking at the cost of this algorithm most likely in terms of edges/vertices as the goal is to construct a minimal spanning tree (which means you need to get all the vertices). If you go with why this works, you will need to analyze the algorithm to find why this theoretically gives you the desired result. You get to choose here as well which part you want to analyze.