Prim's MST

Hi, I am doing an assignment that requires us to do a reverse delete and prim's on a graph. I have already completed the reverse delete and most of the prim's, I just can not figure out how to do a check for cycles. Can anyone point me in the right direction? I'm not looking for code, just some advice. Here's my Edge class:

Code :

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package assignment7;
public class Edge {
    private int weight;
    private char v1;
    private char v2;
    private boolean check;
    public Edge(int weight, char v1, char v2){
        this.weight = weight;
        this.v1 = v1;
        this.v2 = v2;
        this.check = false;
    }
    public char getV1(){
        return this.v1;
    }
    public char getV2(){
        return this.v2;
    }
    public int getWeight(){
        return this.weight;
    }
    public boolean checkIt(){
        return this.check;
    }
    public void change(){
        this.check = true;
    }
}

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The check was used in reverse delete if the edge was visited and could not be deleted. My MST is contained in a Vector<Edge>(suggested by the professor). Thank you for your help.