Disjoint a connected Graph by removing minimum edges.

import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Set;

public class DisJointGraph {
	static Map<Integer, List<Integer>> graph;
	private static Integer noOfVertices = 5;

	static {
		graph = new HashMap<>();
		for (int i = 1; i <= noOfVertices; i++)
			graph.put(i, new ArrayList<>());
	}

	private static void setEdge(Integer verticeA, Integer verticeB) throws Exception {
		if (!graph.containsKey(verticeA)) {
			throw new Exception("Vertice does not exist");
		}
		List<Integer> l = graph.get(verticeA);
		l.add(verticeB);
		graph.put(verticeA, l);
	}

	private static List<Entry<Integer, List<Integer>>> sortByValue() {
		Set<Entry<Integer, List<Integer>>> entrySet = graph.entrySet();
		List<Entry<Integer, List<Integer>>> list = new ArrayList<>(entrySet);
		Collections.sort(list,
				(o1, o2) -> new Integer(o1.getValue().size()).compareTo(new Integer(o2.getValue().size())));
		return list;
	}

	private static void removeEdge() {
		List<Entry<Integer, List<Integer>>> list = sortByValue();
		System.out.println("Sorting List of Vertices and Edges in Reverse order of min edges :: ");
		System.out.println(list);
		graph.remove(list.get(0).getKey());
	}

	private static void printGraph() {
		System.out.println(graph);
	}

	public static void main(String[] args) throws Exception {
		setEdge(1, 2);
		setEdge(1, 3);
		setEdge(2, 3);
		setEdge(2, 4);
		setEdge(2, 5);
		setEdge(3, 1);
		setEdge(3, 2);
		setEdge(3, 5);
		setEdge(4, 2);
		setEdge(5, 2);
		setEdge(5, 3);
		System.out.println("Input Graph Vertices and Edges :: ");
		printGraph();
		removeEdge();
		System.out.println("Output Graph after remove the edge and making the graph disjoint :: ");
		System.out.println(graph);

	}
}