/**
* This method will return a list of vertices which represents the Eulerian circuit of the graph.
*
* @param g The graph to find an Eulerian circuit
* @return null if no Eulerian circuit exists, or a list of vertices representing the Eulerian
* circuit if one does exist
*/
public static <V, E> List<V> getEulerianCircuitVertices(UndirectedGraph<V, E> g) {
// If the graph is not Eulerian then just return a null since no
// Eulerian circuit exists
if (!isEulerian(g)) {
return null;
}
// The circuit will be represented by a linked list
List<V> path = new LinkedList<V>();
UndirectedGraph<V, E> sg = new UndirectedSubgraph<V, E>(g, null, null);
path.add(sg.vertexSet().iterator().next());
// Algorithm for finding an Eulerian circuit Basically this will find an
// arbitrary circuit, then it will find another arbitrary circuit until
// every edge has been traversed
while (sg.edgeSet().size() > 0) {
V v = null;
// Find a vertex which has an edge that hasn't been traversed yet,
// and keep its index position in the circuit list
int index = 0;
for (Iterator<V> iter = path.iterator(); iter.hasNext(); index++) {
v = iter.next();
if (sg.degreeOf(v) > 0) {
break;
}
}
// Finds an arbitrary circuit of the current vertex and
// appends this into the circuit list
while (sg.degreeOf(v) > 0) {
for (Iterator<V> iter = sg.vertexSet().iterator(); iter.hasNext(); ) {
V temp = iter.next();
if (sg.containsEdge(v, temp)) {
path.add(index, temp);
sg.removeEdge(v, temp);
v = temp;
break;
}
}
}
}
return path;
}
/**
* This method will check whether the graph passed in is Eulerian or not.
*
* @param g The graph to be checked
* @return true for Eulerian and false for non-Eulerian
*/
public static <V, E> boolean isEulerian(UndirectedGraph<V, E> g) {
// If the graph is not connected, then no Eulerian circuit exists
if (!(new ConnectivityInspector<V, E>(g)).isGraphConnected()) {
return false;
}
// A graph is Eulerian if and only if all vertices have even degree
// So, this code will check for that
Iterator<V> iter = g.vertexSet().iterator();
while (iter.hasNext()) {
V v = iter.next();
if ((g.degreeOf(v) % 2) == 1) {
return false;
}
}
return true;
}