org.graphstream.algorithm
Class PageRank

java.lang.Object
  org.graphstream.algorithm.PageRank

All Implemented Interfaces:

Algorithm, DynamicAlgorithm, org.graphstream.stream.ElementSink

public class PageRank
extends Object
implements DynamicAlgorithm, org.graphstream.stream.ElementSink

The PageRank is an algorithm that measures the "importance" of the nodes in a graph. It assigns to each node a rank. This rank corresponds to the probability that a "random surfer" visits the node. The surfer goes from node to node in the following way: with probability d she chooses a random outgoing arc and with probability 1 - d she "teleports" to a random node (possibly not connected to the current). The probability d is called damping factor. By default it is 0.85 but it can be customized (see setDampingFactor(double)). The ranks are real numbers between 0 and 1 and sum up to one.

Usage

This implementation uses a variant of the power iteration algorithm to compute the node ranks. It computes the approximate ranks iteratively going closer to the exact values at each iteration. The accuracy can be controlled by a precision parameter (see setPrecision(double)). When the L1 norm of the difference between two consecutive rank vectors becomes less than this parameter, the result is considered precise enough and the computation stops.

This implementation works with both directed and undirected edges. An undirected edge acts as two directed arcs.

The graph dynamics is taken into account and the ranks are not computed from scratch at each modification in the structure of the graph. However, the ranks become less and less accurate after each modification. To establish the desired precision, one must either explicitly call compute() or ask for a rank of a node by calling getRank(Node).

The computed ranks are stored in node attribute. The name of this attribute can be changed by a call to setRankAttribute(String) but only before the call to init(Graph). Another way to obtain the ranks is to call getRank(Node). The second method is preferable because it will update the ranks if needed and will always return values within the desired precision.

Example

 Graph graph = new SingleGraph("test");
 graph.addAttribute("ui.antialias", true);
 graph.addAttribute("ui.stylesheet",
                "node {fill-color: red; size-mode: dyn-size;} edge {fill-color:grey;}");
 graph.display();
 
 DorogovtsevMendesGenerator generator = new DorogovtsevMendesGenerator();
 generator.setDirectedEdges(true, true);
 generator.addSink(graph);
 
 PageRank pageRank = new PageRank();
 pageRank.init(graph);
 
 generator.begin();
 while (graph.getNodeCount() < 100) {
        generator.nextEvents();
        for (Node node : graph) {
                double rank = pageRank.getRank(node);
                node.addAttribute("ui.size",
                                5 + Math.sqrt(graph.getNodeCount() * rank * 20));
                node.addAttribute("ui.label", String.format("%.2f%%", rank * 100));
        }
        Thread.sleep(1000);
 }
 

Computational Complexity :

Each iteration takes O(m + n) time, where n is the number of nodes and m is the number of edges. The number of iterations needed to converge depends on the desired precision.

Scientific Reference :

Lawrence Page, Sergey Brin, Rajeev Motwani and Terry Winograd. The PageRank citation ranking: Bringing order to the Web. 1999

Field Summary

static double	DEFAULT_DAMPING_FACTOR Default damping factor
static double	DEFAULT_PRECISION Default precision
static String	DEFAULT_RANK_ATTRIBUTE Default rank attribute

Constructor Summary

PageRank()
Creates a new instance.

PageRank(double dampingFactor, double precision, String rankAttribute)
Creates a new instance.

Method Summary

void	compute() Run the algorithm.
void	edgeAdded(String sourceId, long timeId, String edgeId, String fromNodeId, String toNodeId, boolean directed)
void	edgeRemoved(String sourceId, long timeId, String edgeId)
double	getDampingFactor() Returns the current damping factor.
int	getIterationCount() Returns the total number of iterations.
double	getPrecision() Returns the currently used numeric precision
double	getRank(org.graphstream.graph.Node node) Returns the rank of a node.
String	getRankAttribute() Returns the current rank attribute
void	graphCleared(String sourceId, long timeId)
void	init(org.graphstream.graph.Graph graph) Initialization of the algorithm.
void	nodeAdded(String sourceId, long timeId, String nodeId)
void	nodeRemoved(String sourceId, long timeId, String nodeId)
void	setDampingFactor(double dampingFactor) Sets the damping factor.
void	setPrecision(double precision) Sets the numeric precision.
void	setRankAttribute(String rankAttribute) Sets the rank attribute.
void	setVerbose(boolean verbose) Switches on or off the verbose mode.
void	stepBegins(String sourceId, long timeId, double step)
void	terminate() Terminate the dynamic algorithm.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

DEFAULT_DAMPING_FACTOR

public static final double DEFAULT_DAMPING_FACTOR

Default damping factor

See Also:

Constant Field Values

DEFAULT_PRECISION

public static final double DEFAULT_PRECISION

Default precision

See Also:

Constant Field Values

DEFAULT_RANK_ATTRIBUTE

public static final String DEFAULT_RANK_ATTRIBUTE

Default rank attribute

See Also:

Constant Field Values

Constructor Detail

PageRank

public PageRank()

Creates a new instance. The damping factor, the precision and the rank attribute are set to their default values

PageRank

public PageRank(double dampingFactor,
                double precision,
                String rankAttribute)

Creates a new instance.

Parameters:

dampingFactor - Damping factor

precision - Numeric precision

rankAttribute - Rank attribute

Method Detail

getDampingFactor

public double getDampingFactor()

Returns the current damping factor.

Returns:

The current damping factor

setDampingFactor

public void setDampingFactor(double dampingFactor)
                      throws IllegalArgumentException

Sets the damping factor.

Parameters:

dampingFactor - The new damping factor

Throws:

IllegalArgumentException - If the damping factor is less than 0.01 or greater than 0.99

getPrecision

public double getPrecision()

Returns the currently used numeric precision

Returns:

The precision

setPrecision

public void setPrecision(double precision)
                  throws IllegalArgumentException

Sets the numeric precision. Precision values close to zero lead to more accurate results, but slower convergence

Parameters:

precision - The new precision

Throws:

IllegalArgumentException - if the precision is less than 1.0e-7

getRankAttribute

public String getRankAttribute()

Returns the current rank attribute

Returns:

The current rank attribute

setRankAttribute

public void setRankAttribute(String rankAttribute)
                      throws IllegalStateException

Sets the rank attribute. The computed ranks of each node are stored as values of this attribute.

Parameters:

rankAttribute - The node attribute used to store the computed ranks

Throws:

IllegalStateException - if the algorithm is already initialized

setVerbose

public void setVerbose(boolean verbose)

Switches on or off the verbose mode. In verbose mode the algorithm prints at each iteration the number of iterations and the L1 norm of the difference between the current and the previous rank vectors.

Parameters:

verbose - Verbose mode

init

public void init(org.graphstream.graph.Graph graph)

Description copied from interface: Algorithm

Initialization of the algorithm. This method has to be called before the Algorithm.compute() method to initialize or reset the algorithm according to the new given graph.

Specified by:

init in interface Algorithm

Parameters:

graph - The graph this algorithm is using.

compute

public void compute()

Description copied from interface: Algorithm

Run the algorithm. The Algorithm.init(Graph) method has to be called before computing.

Specified by:

compute in interface Algorithm

See Also:

Algorithm.init(Graph)

terminate

public void terminate()

Description copied from interface: DynamicAlgorithm

Terminate the dynamic algorithm.

Specified by:

terminate in interface DynamicAlgorithm

See Also:

Algorithm.init(org.graphstream.graph.Graph)

nodeAdded

public void nodeAdded(String sourceId,
                      long timeId,
                      String nodeId)

Specified by:

nodeAdded in interface org.graphstream.stream.ElementSink

nodeRemoved

public void nodeRemoved(String sourceId,
                        long timeId,
                        String nodeId)

Specified by:

nodeRemoved in interface org.graphstream.stream.ElementSink

edgeAdded

public void edgeAdded(String sourceId,
                      long timeId,
                      String edgeId,
                      String fromNodeId,
                      String toNodeId,
                      boolean directed)

Specified by:

edgeAdded in interface org.graphstream.stream.ElementSink

edgeRemoved

public void edgeRemoved(String sourceId,
                        long timeId,
                        String edgeId)

Specified by:

edgeRemoved in interface org.graphstream.stream.ElementSink

graphCleared

public void graphCleared(String sourceId,
                         long timeId)

Specified by:

graphCleared in interface org.graphstream.stream.ElementSink

stepBegins

public void stepBegins(String sourceId,
                       long timeId,
                       double step)

Specified by:

stepBegins in interface org.graphstream.stream.ElementSink

getRank

public double getRank(org.graphstream.graph.Node node)

Returns the rank of a node. If the ranks are not up to date, recomputes them

Parameters:

node - A node

Returns:

The rank of the node

getIterationCount

public int getIterationCount()

Returns the total number of iterations. This number accumulates the number of iterations performed by each call to compute(). It is reset to zero in the calls to init(Graph).

Returns:

The number of iterations