public EdgeBetweennessGraph(WeightedMultigraph<String, DefaultWeightedEdge> originalGraph) {
super(DefaultWeightedEdge.class); // Constructor inherented from parent class
// 1. Initialize the edge betweenness digraph
// 1.1. Add vertices
for (String thisVertex : originalGraph.vertexSet()) this.addVertex(thisVertex);
// 1.2. Add edges
for (DefaultWeightedEdge thisEdge : originalGraph.edgeSet()) {
DefaultWeightedEdge newEdge = new DefaultWeightedEdge();
String sendingName = originalGraph.getEdgeSource(thisEdge);
String receivingName = originalGraph.getEdgeTarget(thisEdge);
this.addEdge(sendingName, receivingName, newEdge);
this.setEdgeWeight(newEdge, 0.0);
}
// 1.3. Create corresponding unweighted graph
// 1.3.1. Add vertices
WeightedMultigraph<String, DefaultWeightedEdge> originalUnweightedGraph =
new WeightedMultigraph<String, DefaultWeightedEdge>(DefaultWeightedEdge.class);
for (String thisVertex : originalGraph.vertexSet())
originalUnweightedGraph.addVertex(thisVertex);
// 1.3.2. Add edges
for (DefaultWeightedEdge thisEdge : originalGraph.edgeSet()) {
DefaultWeightedEdge newEdge = new DefaultWeightedEdge();
String sendingName = originalGraph.getEdgeSource(thisEdge);
String receivingName = originalGraph.getEdgeTarget(thisEdge);
originalUnweightedGraph.addEdge(sendingName, receivingName, newEdge);
originalUnweightedGraph.setEdgeWeight(newEdge, 1.0);
}
for (String thisVertex : this.vertexSet()) {
// 2. Create shortest-path graph for every vertex by Dijkstra algorithm
Multigraph<String, DefaultEdge> shortestPathDigraph =
DijkstraAlgorithm(originalUnweightedGraph, thisVertex);
// 3. Calculate the contribution of current vertex's shortest-path graph to final edge
// betweenness (Newman algorithm)
SimpleWeightedGraph<String, DefaultWeightedEdge> edgeBetweennessDigraph =
NewmanAlgorithm(shortestPathDigraph, thisVertex);
// 4. Update final edge betweenness digraph with current vertex's shortest-path graph
if (edgeBetweennessDigraph != null)
for (DefaultWeightedEdge thisEdge : edgeBetweennessDigraph.edgeSet()) {
String sourceVertex = edgeBetweennessDigraph.getEdgeSource(thisEdge);
String targetVertex = edgeBetweennessDigraph.getEdgeTarget(thisEdge);
double betweennessWeight = edgeBetweennessDigraph.getEdgeWeight(thisEdge);
DefaultWeightedEdge edgeInWholeGraph = this.getEdge(sourceVertex, targetVertex);
double newWeight = this.getEdgeWeight(edgeInWholeGraph) + betweennessWeight;
this.setEdgeWeight(edgeInWholeGraph, newWeight);
}
}
// 5. Revise the edge betweenness digraph with the original active power digraph
for (DefaultWeightedEdge thisEdge : this.edgeSet()) {
String sourceVertex = this.getEdgeSource(thisEdge);
String targetVertex = this.getEdgeTarget(thisEdge);
double betweennessWeight = this.getEdgeWeight(thisEdge);
DefaultWeightedEdge edgeInWholeGraph = originalGraph.getEdge(sourceVertex, targetVertex);
double newWeight = betweennessWeight / originalGraph.getEdgeWeight(edgeInWholeGraph);
this.setEdgeWeight(thisEdge, newWeight);
// System.out.println("Final edge betweenness between " + sourceVertex + " and " +
// targetVertex + ": " + newWeight);
}
}
// Create shortest-path graph for every vertex by depth-first traversal algorithm
private Multigraph<String, DefaultEdge> DijkstraAlgorithm(
WeightedMultigraph<String, DefaultWeightedEdge> originalGraph, String thisVertex) {
// 1. Simplify the multi-graph of the active power flow into a simple graph
SimpleWeightedGraph<String, DefaultWeightedEdge> originalSimpleGraph =
new SimpleWeightedGraph<String, DefaultWeightedEdge>(DefaultWeightedEdge.class);
for (String curVertex : originalGraph.vertexSet()) originalSimpleGraph.addVertex(curVertex);
for (DefaultWeightedEdge curEdge : originalGraph.edgeSet()) {
String sourceVertex = originalGraph.getEdgeSource(curEdge);
String targetVertex = originalGraph.getEdgeTarget(curEdge);
if (originalSimpleGraph.containsEdge(sourceVertex, targetVertex)) {
DefaultWeightedEdge modifiedEdge = originalSimpleGraph.getEdge(sourceVertex, targetVertex);
double newEdgeWeight =
originalSimpleGraph.getEdgeWeight(modifiedEdge) + originalGraph.getEdgeWeight(curEdge);
originalSimpleGraph.setEdgeWeight(modifiedEdge, newEdgeWeight);
} else {
DefaultWeightedEdge newEdge = new DefaultWeightedEdge();
originalSimpleGraph.addEdge(sourceVertex, targetVertex, newEdge);
originalSimpleGraph.setEdgeWeight(newEdge, originalGraph.getEdgeWeight(curEdge));
}
}
// Issue (2010/10/25): Maybe larger amount of active power transfer still means weaker
// relationship between the two terminal buses of a certain branch,
// thus originalSimpleGraph other than inverseGraph should be used here.
// Use the inverse of active power to build a new weighted directed graph (the larger the active
// power is, the close the two buses will be)
// SimpleDirectedWeightedGraph<String, DefaultWeightedEdge> inverseGraph =
// new SimpleDirectedWeightedGraph<String, DefaultWeightedEdge>(DefaultWeightedEdge.class);
// for (String curVertex : originalSimpleGraph.vertexSet())
// inverseGraph.addVertex(curVertex);
// for (DefaultWeightedEdge curEdge : originalSimpleGraph.edgeSet()) {
// String sourceVertex = originalSimpleGraph.getEdgeSource(curEdge);
// String targetVertex = originalSimpleGraph.getEdgeTarget(curEdge);
// DefaultWeightedEdge newEdge = new DefaultWeightedEdge();
// inverseGraph.addEdge(sourceVertex, targetVertex, newEdge);
// inverseGraph.setEdgeWeight(newEdge, 1 / originalSimpleGraph.getEdgeWeight(curEdge));
// }
// 2. Initialize the map of vertices and the corresponding weights (distance from current vertex
// to the first vertex)
HashMap<String, Double> mapVertexShortestDistance = new HashMap<String, Double>();
// for (String thisOriginalVertex : inverseGraph.vertexSet())
for (String thisOriginalVertex : originalSimpleGraph.vertexSet())
mapVertexShortestDistance.put(thisOriginalVertex, 10E10);
// The weight of the first vertex is zero
mapVertexShortestDistance.put(thisVertex, 0.0);
// 3. Depth-first traversing, update the shortest-path values
Stack<String> bfiVertices =
new Stack<String>(); // Stack to store passed vertices in a breadth-first traversing
// The map of a weighted edge and the flag of having been visited
// HashMap<DefaultWeightedEdge, Boolean> mapEdgeVisited = new HashMap<DefaultWeightedEdge,
// Boolean>();
// for (DefaultWeightedEdge thisEdge : inverseGraph.edgeSet())
// mapEdgeVisited.put(thisEdge, false);
String currentVertex = thisVertex;
bfiVertices.push(currentVertex);
// System.out.println(bfiVertices.toString());
while (!bfiVertices.isEmpty()) {
// Operate the following codes for those edges started with current vertex
boolean hasNewEdge = false;
// for (DefaultWeightedEdge curEdge : inverseGraph.outgoingEdgesOf(currentVertex)) {
for (DefaultWeightedEdge curEdge : originalSimpleGraph.edgesOf(currentVertex)) {
// if (!mapEdgeVisited.get(curEdge)) { // Used for those edges that have not been treated
// yet
// 3.1. Mark current edge as already been visited
// mapEdgeVisited.put(curEdge, true);
// String nextVertex = inverseGraph.getEdgeTarget(curEdge);
String nextVertex = originalSimpleGraph.getEdgeTarget(curEdge);
// 3.2. Update shortest-path values
double curSD = mapVertexShortestDistance.get(currentVertex);
// double edgeWeight = inverseGraph.getEdgeWeight(curEdge);
double edgeWeight = originalSimpleGraph.getEdgeWeight(curEdge);
double newSD = curSD + edgeWeight;
if (mapVertexShortestDistance.get(nextVertex) > newSD) {
hasNewEdge = true;
mapVertexShortestDistance.put(nextVertex, newSD);
// 3.3. Push the target vertex of current edge into the stack
bfiVertices.push(nextVertex);
// System.out.println(bfiVertices.toString());
break;
// System.out.println("New shortest path [" + nextVertex + "]: " + newSD);
}
// }
}
if (!hasNewEdge) {
bfiVertices.pop();
}
if (!bfiVertices.isEmpty()) currentVertex = bfiVertices.peek();
}
// 4. Create shortest-path digraph of current vertex
// 4.1. Initialize the shortest-path digraph
Multigraph<String, DefaultEdge> shortestPathGraph =
new Multigraph<String, DefaultEdge>(DefaultEdge.class);
// 4.2. Add all qualified edges
// for (DefaultWeightedEdge curEdge : inverseGraph.edgeSet()) {
for (DefaultWeightedEdge curEdge : originalSimpleGraph.edgeSet()) {
// 4.2.1. Evaluate if current edge is suitable
// String sourceVertex = inverseGraph.getEdgeSource(curEdge);
// String targetVertex = inverseGraph.getEdgeTarget(curEdge);
String sourceVertex = originalSimpleGraph.getEdgeSource(curEdge);
String targetVertex = originalSimpleGraph.getEdgeTarget(curEdge);
// if (Math.abs(inverseGraph.getEdgeWeight(curEdge) -
if (originalSimpleGraph.getEdgeWeight(curEdge) > 1.0E-5) {
if (Math.abs(
originalSimpleGraph.getEdgeWeight(curEdge)
- (mapVertexShortestDistance.get(targetVertex)
- mapVertexShortestDistance.get(sourceVertex)))
< 1.0E-5) {
// 4.2.2. Add suitable edge that found just now
DefaultEdge newEdge = new DefaultEdge();
if (!shortestPathGraph.containsVertex(sourceVertex))
shortestPathGraph.addVertex(sourceVertex);
if (!shortestPathGraph.containsVertex(targetVertex))
shortestPathGraph.addVertex(targetVertex);
shortestPathGraph.addEdge(sourceVertex, targetVertex, newEdge);
}
}
}
return shortestPathGraph;
}