Problem: determine if a graph has cycles:

import java.util.*;

import java.lang.*;

import java.io.*;

class Ideone

{

 public static void main (String[] args) throws java.lang.Exception

 {

  int[][] m = new int[5][5]();

  for (int i = 0; i < m.length; i++) {

   for (int j = 0; j < m[0].length; j++) {

    m[i][j] = 0;

   }

  }

  m[0][1] = 1;

  m[0][2] = 1;

  m[1][0] = 1;

  m[1][3] = 1;

  m[2][0] = 1;

  m[2][3] = 1;

  m[3][1] = 1;

  m[3][2] = 1;

  m[3][4] = 1;

  m[4][3] = 1;

  var vertices = InitializeSingleSource(m, 0);

  var edges = new HashMap<String, String>();

  edges.put("A", "B");

  edges.put("A", "C");

  edges.put("B", "A");

  edges.put("B", "D");

  edges.put("C", "A");

  edges.put("C", "D");

  edges.put("D", "B");

  edges.put("D", "C");

  edges.put("D", "E");

  edges.put("E", "D");

  System.out.println(hasCyclesByBellmanFord(vertices, edges));

 }

 private static List<Vertex> InitializeSingleSource(int[][] m, int start) {

  var vertices = new ArrayList<Vertex>();

  for (int i = 0; i < m.length; i++){

   var v = new Vertex();

   v.id = String.valueOf(Character.valueOf('A' + i));

   v.d = Integer.MAX_VALUE;

   if (i == start) { v.d = 0; }

   v.parent = null;

  }

  return vertices

 }

 private static Vertex getVertex(List<Vertex> vertices, String id){

  for (int i = 0; i < vertices.size(); i++){

   if (vertices.get(i).id.equals(id)){

    return vertices.get(i);

   }

  }

  return null;

 }

 // A ->C <-D ->E

 // ->B->

 private static boolean hasCyclesByBellmanFord(List<Vertex> vertices, Map<String, String> edgeMap) {

  boolean result = false;

  for (int i = 0; i < vertices.length; i++){

   for(var entry: edgeMap.entrySet()) {

    var u = getVertex(entry.getKey());

    var v = getVertex(entry.getValue());

    relax(u, v);

   }

  }

  for (var entry: edgeMap.entrySet()) {

   var u = getVertex(entry.getKey());

   var v = getVertex(entry.getValue());

   if (u != null &&

    v != null &&

    v.d > u.d + 1) {

    result = true;

    return result;

   }

  }

  return result;

 }

 private static void Relax(Vertex u, Vertex v) {

  if (u == null || v == null) { return; }

  if (v.d > u.d + 1) {

   v.d = u.d + 1;

   v.parent = u;

  }

 }

 class Vertex {

  public String id;

  public Vertex parent;

  public Integer d;

 }

}