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Centrality.java
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Centrality.java
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import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Stack;
/**
* A class containing several methods to compute the centrality of a given
* graph. This includes degree centrality, closeness centrality, betweenness
* centrality and Katz centrality. This class utilizes the graph class'
* representation of a graph.
* @author Bruce How (22242664) & Haolin Wu (21706137)
*/
public class Centrality {
/**
* Returns an array of integer ArrayList, containing the nodes with the
* highest degree centrality, for each component of the graph. This is the
* node which has the highest number of incident edges.
* @param graph The graph to be checked
* @return An array of nodes with the highest degree centrality for each
* component
*/
public ArrayList<ArrayList<Integer>> degreeCentrality(Graph graph) {
int componentSize = graph.getComponents().size();
ArrayList<ArrayList<Integer>> degree = new ArrayList<>();
for (int i = 0; i < componentSize; i++) {
// stores the degree centrality value for each node
ArrayList<Node> centralityValue = new ArrayList<>();
for (int node : graph.getComponents().get(i)) {
int incidentNodes = graph.getConnectedNodes(node).size();
centralityValue.add(new Node(node, incidentNodes));
}
// sorts the nodes according to its degree centrality
ArrayList<Integer> results = new ArrayList<>();
Collections.sort(centralityValue, Collections.reverseOrder());
Iterator<Node> it = centralityValue.iterator();
while (it.hasNext() && results.size() < 5) {
results.add((int) it.next().id);
}
degree.add(results);
}
return degree;
}
/**
* Performs a BFS on a given graph to fetch the nodes with the highest
* closeness centrality for each component of the graph. This is the node
* with the smallest average shortest paths to all other nodes in the graph.
* @param graph The graph to be checked
* @return An array of nodes with the highest closeness centrality for each
* component
*/
public ArrayList<ArrayList<Integer>> closenessCentrality(Graph graph) {
int componentSize = graph.getComponents().size();
ArrayList<ArrayList<Integer>> closeness = new ArrayList<>();
for (int i = 0; i < componentSize; i++) {
// stores the closeness centrality value for each node
ArrayList<Node> centralityValue = new ArrayList<>();
ArrayList<Integer> component = graph.getComponents().get(i);
for (Integer source : component) {
/*
* Runs a BFS algorithm on the graph to find the shortest
* distances to all other nodes from the current source node
*/
HashMap<Integer, Integer> distance = new HashMap<>();
Queue<Integer> queue = new LinkedList<>();
distance.put(source, 0);
int current = source;
while (distance.size() != component.size()) {
for (Integer node : graph.getConnectedNodes(current)) {
if (!distance.containsKey(node)) {
distance.put(node, distance.get(current) + 1);
queue.add(node);
}
}
if (!queue.isEmpty()) {
current = queue.poll();
}
}
/*
* Caculate total SP distance from source to each node and adds
* it to the centralityValue ArrayList.
*/
int totalDistance = 0;
for (Integer nodeDistance : distance.values()) {
totalDistance += nodeDistance;
}
centralityValue.add(new Node(source, totalDistance));
}
// sorts the nodes according to its closeness centrality
ArrayList<Integer> results = new ArrayList<>();
// values represent far(j) thus reverse sort is not needed
Collections.sort(centralityValue);
Iterator<Node> it = centralityValue.iterator();
while (it.hasNext() && results.size() < 5) {
results.add((int) it.next().id);
}
closeness.add(results);
}
return closeness;
}
/**
* Performs Brandes algorithm on a given graph to fetch the nodes with the
* highest bewtweenness centrality for each component of the graph. This is
* the node which passes through the most shortest paths in a graph
* @param graph The graph to be checked
* @return An array of nodes with the highest closeness centrality for each
* component.
*/
public ArrayList<ArrayList<Integer>> betweennessCentrality(Graph graph) {
int componentSize = graph.getComponents().size();
ArrayList<ArrayList<Integer>> betweenness = new ArrayList<>();
for (int i = 0; i < componentSize; i++) {
ArrayList<Integer> component = graph.getComponents().get(i);
// stores the betweenness Centrality value for each node
HashMap<Integer, Double> centrality = new HashMap<>();
for (Integer source : component) {
/*
* Runs a BFS algorithm on the graph to find the shortest
* distances to all other nodes, preceding nodes that pass
* within all the SP, and number of SP from the source node
*/
Stack<Integer> stack = new Stack<>();
Queue<Integer> queue = new LinkedList<>();
HashMap<Integer, ArrayList<Integer>> precedingNode = new HashMap<>();
HashMap<Integer, Integer> distance = new HashMap<>();
HashMap<Integer, Integer> paths = new HashMap<>();
queue.add(source);
paths.put(source, 1);
distance.put(source, 0);
while (!queue.isEmpty()) {
int current = queue.poll();
// used for the dependency accumulation algorithm later
stack.push(current);
for (Integer node : graph.getConnectedNodes(current)) {
// node is founded for the first time
if (!distance.containsKey(node)) {
queue.add(node);
distance.put(node, distance.get(current) + 1);
paths.put(node, paths.get(current));
ArrayList<Integer> parent = new ArrayList<>();
parent.add(current);
precedingNode.put(node, parent);
// found another SP for existing node
} else if (distance.get(node) == distance.get(current) + 1) {
paths.put(node, (paths.get(node) + paths.get(current)));
ArrayList<Integer> precede = precedingNode.get(node);
precede.add(current);
precedingNode.put(node, precede);
}
}
}
/*
* Runs Brandes' dependency accumulation algorithm to compute
* the betweenness centrality for each node.
*/
HashMap<Integer, Double> dependency = new HashMap<>();
for (Integer node : component) {
dependency.put(node, 0.0);
}
while (!stack.isEmpty()) {
int current = stack.pop();
if (current != source) {
for (Integer node : precedingNode.get(current)) {
double result = ((double) paths.get(node)
/ paths.get(current)) * (1 + dependency.get(current));
dependency.put(node, dependency.get(node) + result);
}
if (!centrality.containsKey(current)) {
// divided by 2 due to the graph's undirected nature
centrality.put(current, dependency.get(current) / 2);
} else {
centrality.put(current, centrality.get(current)
+ dependency.get(current) / 2);
}
}
}
}
// stores the centrality value for each node as a Node object
ArrayList<Node> centralityValue = new ArrayList<>();
for (Integer node : centrality.keySet()) {
centralityValue.add(new Node(node, centrality.get(node)));
}
// sorts the nodes according to its closeness centrality
ArrayList<Integer> results = new ArrayList<>();
Collections.sort(centralityValue, Collections.reverseOrder());
Iterator<Node> it = centralityValue.iterator();
while (it.hasNext() && results.size() < 5) {
results.add((int) it.next().id);
}
betweenness.add(results);
}
return betweenness;
}
/**
* Performs a BFS on a given graph to fetch the nodes with the highest Katz
* centrality for each component of the graph. This is the node which has
* the highest overall number of edges, that are close by.
* @param graph The graph to be checked
* @return An array of nodes with the highest Katz centrality for each
* component
*/
public ArrayList<ArrayList<Integer>> katzCentrality(Graph graph, double alpha) {
int componentSize = graph.getComponents().size();
ArrayList<ArrayList<Integer>> katz = new ArrayList<>();
for (int i = 0; i < componentSize; i++) {
ArrayList<Integer> component = graph.getComponents().get(i);
// store the centrality value for each node
ArrayList<Node> centralityValue = new ArrayList<>();
for (Integer source : component) {
/*
* Runs a BFS algorithm on the graph to identify the node level
* of each node form the source and compute the Katz centrality
* value for the source
*/
HashMap<Integer, Integer> level = new HashMap<>();
Queue<Integer> queue = new LinkedList<>();
level.put(source, 0);
// stores the Katz centrality value of the source node
double centrality = 0;
int current = source;
while (level.size() != component.size()) {
for (Integer node : graph.getConnectedNodes(current)) {
if (!level.containsKey(node)) {
int newLevel = level.get(current) + 1;
centrality += Math.pow(alpha, newLevel);
level.put(node, newLevel);
queue.add(node);
}
}
if (!queue.isEmpty()) {
current = queue.poll();
}
}
centralityValue.add(new Node(source, centrality));
}
// sorts the nodes according to its closeness centrality
ArrayList<Integer> results = new ArrayList<>();
Collections.sort(centralityValue, Collections.reverseOrder());
Iterator<Node> it = centralityValue.iterator();
while (it.hasNext() && results.size() < 5) {
results.add((int) it.next().id);
}
katz.add(results);
}
return katz;
}
/**
* Private subclass which stores each Node and their respective centrality
* value. This class implements the Comparable interface to compare each
* Node and its respective centrality value
*/
private class Node implements Comparable<Node> {
private int id;
private double value;
/**
* Constructor for the subclass to create a node object
* @param id The node ID
* @param value The centrality value of the node
*/
public Node(int id, double value) {
this.id = id;
this.value = value;
}
/**
* Compares this object with the specified object for ordering
*/
@Override
public int compareTo(Node node) {
return Double.compare(value, node.value);
}
}
}