org.jgrapht.alg.clustering.UndirectedModularityMeasurer Maven / Gradle / Ivy
/*
* (C) Copyright 2020-2023, by Dimitrios Michail and Contributors.
*
* JGraphT : a free Java graph-theory library
*
* See the CONTRIBUTORS.md file distributed with this work for additional
* information regarding copyright ownership.
*
* This program and the accompanying materials are made available under the
* terms of the Eclipse Public License 2.0 which is available at
* http://www.eclipse.org/legal/epl-2.0, or the
* GNU Lesser General Public License v2.1 or later
* which is available at
* http://www.gnu.org/licenses/old-licenses/lgpl-2.1-standalone.html.
*
* SPDX-License-Identifier: EPL-2.0 OR LGPL-2.1-or-later
*/
package org.jgrapht.alg.clustering;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Set;
import java.util.stream.Collectors;
import org.jgrapht.Graph;
import org.jgrapht.GraphTests;
import org.jgrapht.Graphs;
/**
* A modularity measurer.
*
*
* This is a utility class which computes the modularity function. It takes as input a list of
* vertex classes $C$ and a graph $G$ and calculates: $Q = \frac{1}{2m} \sum_{ij} \left( A_{ij} -
* \frac{k_i k_j}{2m} \right) \delta(C_i, C_j)$. Here $m$ is the total number of edges and $k_i$ is
* the degree of vertex $i$. $A_{ij}$ is either $1$ or $0$ depending on whether edge $(i,j)$ belongs
* to the graph and $\delta(C_i, C_j)$ is 1 if vertices $i$ and $j$ belong to the same class, $0$
* otherwise.
*
* @author Dimitrios Michail
*
* @param the vertex type
* @param the edge type
*/
public class UndirectedModularityMeasurer
{
private static final String INVALID_PARTITION_OF_VERTICES = "Invalid partition of vertices";
private final Graph graph;
private double m;
private Map degrees;
/**
* Construct a new measurer
*
* @param graph the input graph
*/
public UndirectedModularityMeasurer(Graph graph)
{
this.graph = GraphTests.requireUndirected(graph);
this.degrees = new HashMap<>();
precomputeDegrees(graph);
}
/**
* Compute the modularity of a vertex partition.
*
* @param partitions the partitions
* @return the modularity
*/
public double modularity(List> partitions)
{
// index partitions and count total (weighted) degree inside each partition
int totalPartitions = partitions.size();
Map vertexPartition = new HashMap<>();
double[] weightedDegreeInPartition = new double[totalPartitions];
int curPartition = 0;
for (Set partition : partitions) {
weightedDegreeInPartition[curPartition] = 0d;
for (V v : partition) {
vertexPartition.put(v, curPartition);
Double d = degrees.get(v);
if (d == null) {
throw new IllegalArgumentException(INVALID_PARTITION_OF_VERTICES);
}
weightedDegreeInPartition[curPartition] += d;
}
curPartition++;
}
// count (weighted) edges inside each partition
double[] edgeWeightInPartition = new double[totalPartitions];
for (E e : graph.edgeSet()) {
V v = graph.getEdgeSource(e);
V u = graph.getEdgeTarget(e);
Integer pv = vertexPartition.get(v);
if (pv == null) {
throw new IllegalArgumentException(INVALID_PARTITION_OF_VERTICES);
}
Integer pu = vertexPartition.get(u);
if (pu == null) {
throw new IllegalArgumentException(INVALID_PARTITION_OF_VERTICES);
}
if (pv.intValue() == pu.intValue()) {
// same partition
edgeWeightInPartition[pv] += graph.getEdgeWeight(e);
}
}
// compute modularity summing over partitions
double mod = 0d;
for (int p = 0; p < totalPartitions; p++) {
double expectedEdgeWeightInPartition =
weightedDegreeInPartition[p] * weightedDegreeInPartition[p] / (2d * m);
mod += 2d * edgeWeightInPartition[p] - expectedEdgeWeightInPartition;
}
mod /= 2d * m;
return mod;
}
/**
* Pre-compute vertex (weighted) degrees.
*
* @param graph the input graph
*/
private void precomputeDegrees(Graph graph)
{
if (graph.getType().isWeighted()) {
m = graph.edgeSet().stream().collect(Collectors.summingDouble(graph::getEdgeWeight));
for (V v : graph.vertexSet()) {
double sum = 0d;
for (E e : graph.outgoingEdgesOf(v)) {
V u = Graphs.getOppositeVertex(graph, e, v);
if (u.equals(v)) {
sum += 2d * graph.getEdgeWeight(e);
} else {
sum += graph.getEdgeWeight(e);
}
}
degrees.put(v, sum);
}
} else {
m = graph.edgeSet().size();
for (V v : graph.vertexSet()) {
// degreeof counts loops twice anyway
degrees.put(v, Double.valueOf(graph.degreeOf(v)));
}
}
}
}