// Calculate the contribution of current vertex's shortest-path graph to final edge betweenness
// (Newman algorithm)
// M. E. J. Newman and M. Girvan, Finding and evaluating community structure in networks, Physical
// Review E69, 026113 (2004)
private SimpleWeightedGraph<String, DefaultWeightedEdge> NewmanAlgorithm(
Multigraph<String, DefaultEdge> shortestPathGraph, String thisVertex) {
if (shortestPathGraph.edgeSet().size() == 0) // No outer degree
return null;
// 1. Initialize the edge betweenness digraph
SimpleWeightedGraph<String, DefaultWeightedEdge> edgeBetweennessDigraph =
new SimpleWeightedGraph<String, DefaultWeightedEdge>(DefaultWeightedEdge.class);
// Add vertices
for (String curVertex : shortestPathGraph.vertexSet())
edgeBetweennessDigraph.addVertex(curVertex);
// 2. Deal with corresponding edges
// 2.1. Calculate vertex distance and weight
// 2.1.1. Initialize related variables
HashMap<String, Integer> mapVertexDistance = new HashMap<String, Integer>(); // Vertex distance
for (String curVertex : shortestPathGraph.vertexSet()) mapVertexDistance.put(curVertex, 0);
HashMap<String, Double> mapVertexWeight = new HashMap<String, Double>(); // Vertex weight
for (String curVertex : shortestPathGraph.vertexSet()) mapVertexWeight.put(curVertex, 1.0);
Queue<String> verticesQueue = new LinkedList<String>(); // Store the queue of operated vertices
// 2.1.2. Traverse the shortest-path digraph, get corresponding vertex distance and weight
verticesQueue.add(thisVertex);
String currentVertex = thisVertex;
while (!verticesQueue.isEmpty()) {
// 2.1.2.1. Read the bottom vertex in the queue, deal with all adjacent edges
for (DefaultEdge curEdge : shortestPathGraph.edgesOf(currentVertex)) {
String targetVertex = shortestPathGraph.getEdgeTarget(curEdge);
if (mapVertexDistance.get(targetVertex)
== 0) { // Target vertex value hasn't been evaluated yet
mapVertexDistance.put(targetVertex, mapVertexDistance.get(currentVertex) + 1);
mapVertexWeight.put(targetVertex, mapVertexWeight.get(currentVertex));
verticesQueue.add(targetVertex);
}
// Target vertex value has already been set to source vertex distance plus 1
else if (mapVertexDistance.get(targetVertex) == (mapVertexDistance.get(currentVertex) + 1))
mapVertexWeight.put(
targetVertex, mapVertexWeight.get(targetVertex) + mapVertexWeight.get(currentVertex));
}
// 2.1.2.2. All adjacent edges have been treated, remove the bottom element
verticesQueue.remove();
currentVertex = verticesQueue.peek();
}
// 2.2. Calculate the contribution of every edges to the edge betweenness
// 2.2.1. Sort the vertices descendingly by the distance to the first vertex
List<Map.Entry<String, Integer>> listVertexDistance =
new ArrayList<Map.Entry<String, Integer>>(mapVertexDistance.entrySet());
Collections.sort(
listVertexDistance,
new Comparator<Map.Entry<String, Integer>>() { // Sorting the list descendingly
@Override
public int compare(Entry<String, Integer> o1, Entry<String, Integer> o2) {
return (o2.getValue().compareTo(o1.getValue()));
}
});
// 2.2.2. Traverse the shortest-path digraph with the sorted vertices list
for (Map.Entry<String, Integer> thisVertexDistance : listVertexDistance) {
currentVertex = thisVertexDistance.getKey();
for (DefaultEdge curEdge : shortestPathGraph.edgesOf(currentVertex)) {
// 2.2.2.1. Get the source vertex
String sourceVertex = shortestPathGraph.getEdgeSource(curEdge);
String targetVertex = shortestPathGraph.getEdgeTarget(curEdge);
String anotherVertex = "";
if (currentVertex.equals(sourceVertex)) anotherVertex = targetVertex;
else if (currentVertex.equals(targetVertex)) anotherVertex = sourceVertex;
// 2.2.2.2. Calculate the value of the sum of all adjacent edges plus 1
double totalSubWeights = 1.0;
for (DefaultWeightedEdge curSubEdge : edgeBetweennessDigraph.edgesOf(currentVertex))
totalSubWeights += edgeBetweennessDigraph.getEdgeWeight(curSubEdge);
// 2.2.2.3. The new edge weight is calculated as totalSubWeights * (the quotient of the
// weights of the two terminals)
double wi = mapVertexWeight.get(anotherVertex);
double wj = mapVertexWeight.get(currentVertex);
totalSubWeights /= wi / wj;
// 2.2.2.4. Add new edge with correct weight into the edge betweenness digraph
DefaultWeightedEdge newEdge = new DefaultWeightedEdge();
edgeBetweennessDigraph.addEdge(anotherVertex, currentVertex, newEdge);
edgeBetweennessDigraph.setEdgeWeight(newEdge, totalSubWeights);
}
}
return edgeBetweennessDigraph;
}
public Set<ApplicationVertex> vertexSet() {
return graph.vertexSet();
}