/**
* Compute the unique decomposition of the input graph G (atoms of G). Implementation of algorithm
* Atoms as described in Berry et al. (2010), DOI:10.3390/a3020197, <a
* href="http://www.mdpi.com/1999-4893/3/2/197">http://www.mdpi.com/1999-4893/3/2/197</a>
*/
private void computeAtoms() {
if (chordalGraph == null) {
computeMinimalTriangulation();
}
separators = new HashSet<>();
// initialize g' as subgraph of graph (same vertices and edges)
UndirectedGraph<V, E> gprime = copyAsSimpleGraph(graph);
// initialize h' as subgraph of chordalGraph (same vertices and edges)
UndirectedGraph<V, E> hprime = copyAsSimpleGraph(chordalGraph);
atoms = new HashSet<>();
Iterator<V> iterator = meo.descendingIterator();
while (iterator.hasNext()) {
V v = iterator.next();
if (generators.contains(v)) {
Set<V> separator = new HashSet<>(Graphs.neighborListOf(hprime, v));
if (isClique(graph, separator)) {
if (separator.size() > 0) {
if (separators.contains(separator)) {
fullComponentCount.put(separator, fullComponentCount.get(separator) + 1);
} else {
fullComponentCount.put(separator, 2);
separators.add(separator);
}
}
UndirectedGraph<V, E> tmpGraph = copyAsSimpleGraph(gprime);
tmpGraph.removeAllVertices(separator);
ConnectivityInspector<V, E> con = new ConnectivityInspector<>(tmpGraph);
if (con.isGraphConnected()) {
throw new RuntimeException("separator did not separate the graph");
}
for (Set<V> component : con.connectedSets()) {
if (component.contains(v)) {
gprime.removeAllVertices(component);
component.addAll(separator);
atoms.add(new HashSet<>(component));
assert (component.size() > 0);
break;
}
}
}
}
hprime.removeVertex(v);
}
if (gprime.vertexSet().size() > 0) {
atoms.add(new HashSet<>(gprime.vertexSet()));
}
}
public void testUndirectedGraphGnp3() {
GraphGenerator<Integer, DefaultEdge, Integer> gen =
new GnpRandomBipartiteGraphGenerator<>(4, 4, 0.0, SEED);
UndirectedGraph<Integer, DefaultEdge> g = new SimpleGraph<>(DefaultEdge.class);
gen.generateGraph(g, new IntegerVertexFactory(), null);
assertEquals(4 + 4, g.vertexSet().size());
assertEquals(0, g.edgeSet().size());
}
/**
* 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;
}
public void testUndirectedGraphGnp1() {
GraphGenerator<Integer, DefaultEdge, Integer> gen =
new GnpRandomBipartiteGraphGenerator<>(4, 4, 0.5, SEED);
UndirectedGraph<Integer, DefaultEdge> g = new SimpleGraph<>(DefaultEdge.class);
gen.generateGraph(g, new IntegerVertexFactory(), null);
int[][] edges = {{1, 6}, {1, 7}, {1, 8}, {2, 5}, {2, 7}, {3, 5}, {3, 8}, {4, 6}, {4, 7}};
assertEquals(4 + 4, g.vertexSet().size());
for (int[] e : edges) {
assertTrue(g.containsEdge(e[0], e[1]));
}
assertEquals(edges.length, g.edgeSet().size());
}
/**
* 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;
}
/**
* Create a copy of a graph for internal use.
*
* @param graph the graph to copy.
* @return A copy of the graph projected to a SimpleGraph.
*/
private static <V, E> UndirectedGraph<V, E> copyAsSimpleGraph(UndirectedGraph<V, E> graph) {
UndirectedGraph<V, E> copy = new SimpleGraph<>(graph.getEdgeFactory());
if (graph instanceof SimpleGraph) {
Graphs.addGraph(copy, graph);
} else {
// project graph to SimpleGraph
Graphs.addAllVertices(copy, graph.vertexSet());
for (E e : graph.edgeSet()) {
V v1 = graph.getEdgeSource(e);
V v2 = graph.getEdgeTarget(e);
if ((v1 != v2) && !copy.containsEdge(e)) {
copy.addEdge(v1, v2);
}
}
}
return copy;
}
/**
* Compute the minimal triangulation of the graph. Implementation of Algorithm MCS-M+ as described
* in Berry et al. (2010), DOI:10.3390/a3020197 <a href="http://www.mdpi.com/1999-4893/3/2/197">
* http://www.mdpi.com/1999-4893/3/2/197</a>
*/
private void computeMinimalTriangulation() {
// initialize chordGraph with same vertices as graph
chordalGraph = new SimpleGraph<>(graph.getEdgeFactory());
for (V v : graph.vertexSet()) {
chordalGraph.addVertex(v);
}
// initialize g' as subgraph of graph (same vertices and edges)
final UndirectedGraph<V, E> gprime = copyAsSimpleGraph(graph);
int s = -1;
generators = new ArrayList<>();
meo = new LinkedList<>();
final Map<V, Integer> vertexLabels = new HashMap<>();
for (V v : gprime.vertexSet()) {
vertexLabels.put(v, 0);
}
for (int i = 1, n = graph.vertexSet().size(); i <= n; i++) {
V v = getMaxLabelVertex(vertexLabels);
LinkedList<V> Y = new LinkedList<>(Graphs.neighborListOf(gprime, v));
if (vertexLabels.get(v) <= s) {
generators.add(v);
}
s = vertexLabels.get(v);
// Mark x reached and all other vertices of gprime unreached
HashSet<V> reached = new HashSet<>();
reached.add(v);
// mark neighborhood of x reached and add to reach(label(y))
HashMap<Integer, HashSet<V>> reach = new HashMap<>();
// mark y reached and add y to reach
for (V y : Y) {
reached.add(y);
addToReach(vertexLabels.get(y), y, reach);
}
for (int j = 0; j < graph.vertexSet().size(); j++) {
if (!reach.containsKey(j)) {
continue;
}
while (reach.get(j).size() > 0) {
// remove a vertex y from reach(j)
V y = reach.get(j).iterator().next();
reach.get(j).remove(y);
for (V z : Graphs.neighborListOf(gprime, y)) {
if (!reached.contains(z)) {
reached.add(z);
if (vertexLabels.get(z) > j) {
Y.add(z);
E fillEdge = graph.getEdgeFactory().createEdge(v, z);
fillEdges.add(fillEdge);
addToReach(vertexLabels.get(z), z, reach);
} else {
addToReach(j, z, reach);
}
}
}
}
}
for (V y : Y) {
chordalGraph.addEdge(v, y);
vertexLabels.put(y, vertexLabels.get(y) + 1);
}
meo.addLast(v);
gprime.removeVertex(v);
vertexLabels.remove(v);
}
}