Package it.unimi.dsi.webgraph.algo

Class NeighbourhoodFunction

java.lang.Object
it.unimi.dsi.webgraph.algo.NeighbourhoodFunction
public class NeighbourhoodFunction
extends Object
Computes the neighbourhood function of a graph by multiple parallel breadth-first visits.

Note that performing all breadth-first visits requires time O(nm), so this class is usable only on very small graphs.

Additionally, this class provides several useful static methods such as distanceCumulativeDistributionFunction(double[]), distanceProbabilityMassFunction(double[]), averageDistance(double[]), medianDistance(int, double[]) and spid(double[]) that act on neighbourhood functions.

Performance issues

This class uses an instance of ParallelBreadthFirstVisit to ensure a high degree of parallelism (see its documentation for memory requirements). Note that if the graph is small a large number of thread will slow down the computation because of synchronization costs.

Author:
Paolo Boldi, Sebastiano Vigna

  • Constructor Summary

    Constructors
    Constructor Description
    NeighbourhoodFunction()  

  • Method Summary

    Modifier and Type Method Description
    static double averageDistance​(double[] neighbourhoodFunction)
    Returns the average of the distances between reachable pairs of nodes.
    static double[] compute​(ImmutableGraph g)
    Computes and returns the neighbourhood function of the specified graph by multiple breadth-first visits.
    static double[] compute​(ImmutableGraph g, int threads, ProgressLogger pl)
    Computes and returns the neighbourhood function of the specified graph by multiple breadth-first visits.
    static double[] compute​(ImmutableGraph g, ProgressLogger pl)
    Computes and returns the neighbourhood function of the specified graph by multiple breadth-first visits.
    static long[] computeExact​(ImmutableGraph g, int threads, ProgressLogger pl)
    Computes and returns the neighbourhood function of the specified graph by multiple breadth-first visits.
    static double[] distanceCumulativeDistributionFunction​(double[] neighbourhoodFunction)
    Returns the distance cumulative distribution function.
    static double[] distanceProbabilityMassFunction​(double[] neighbourhoodFunction)
    Returns the probability mass function of the distance distribution.
    static double effectiveDiameter​(double[] neighbourhoodFunction)
    Returns the effective diameter at 0.9.
    static double effectiveDiameter​(double alpha, double[] neighbourhoodFunction)
    Returns the effective diameter at a specified fraction.
    static double harmonicDiameter​(double[] neighbourhoodFunction)
    Returns the harmonic diameter, that is, the harmonic mean of all distances.
    static double harmonicDiameter​(int n, double[] neighbourhoodFunction)
    Returns the harmonic diameter, that is, the harmonic mean of all distances.
    static void main​(String[] arg)  
    static double medianDistance​(double[] neighbourhoodFunction)
    Returns the median of distances between all pairs of nodes.
    static double medianDistance​(int n, double[] neighbourhoodFunction)
    Returns the median of distances between all pairs of nodes.
    static double spid​(double[] neighbourhoodFunction)
    Returns the spid (shortest-paths index of dispersion).

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • NeighbourhoodFunction

      public NeighbourhoodFunction()

  • Method Details

    • compute

      public static double[] compute​(ImmutableGraph g)
      Computes and returns the neighbourhood function of the specified graph by multiple breadth-first visits.

      This method returns an array of doubles. When some values of the function are near 263, it might lose some least-significant digits. If you need exact values, use computeExact(ImmutableGraph, int, ProgressLogger) instead.

      Parameters:
      g - a graph.
      Returns:
      the neighbourhood function of the specified graph.

    • compute

      public static double[] compute​(ImmutableGraph g, ProgressLogger pl)
      Computes and returns the neighbourhood function of the specified graph by multiple breadth-first visits.

      This method returns an array of doubles. When some values of the function are near 263, it might lose some least-significant digits. If you need exact values, use computeExact(ImmutableGraph, int, ProgressLogger) instead.

      Parameters:
      g - a graph.
      pl - a progress logger, or null.
      Returns:
      the neighbourhood function of the specified graph.

    • compute

      public static double[] compute​(ImmutableGraph g, int threads, ProgressLogger pl)
      Computes and returns the neighbourhood function of the specified graph by multiple breadth-first visits.

      This method returns an array of doubles. When some values of the function are near 263, it might lose some least-significant digits. If you need exact values, use computeExact(ImmutableGraph, int, ProgressLogger) instead.

      Parameters:
      g - a graph.
      threads - the requested number of threads (0 for Runtime.availableProcessors()). Note that if the graph is small a large number of thread will slow down the computation because of synchronization costs.
      pl - a progress logger, or null.
      Returns:
      the neighbourhood function of the specified graph.

    • computeExact

      public static long[] computeExact​(ImmutableGraph g, int threads, ProgressLogger pl)
      Computes and returns the neighbourhood function of the specified graph by multiple breadth-first visits.

      This method returns an array of longs. When some values of the function are near 263, it provides an exact value, as opposed to compute(ImmutableGraph, int, ProgressLogger).

      Parameters:
      g - a graph.
      threads - the requested number of threads (0 for Runtime.availableProcessors()). Note that if the graph is small a large number of thread will slow down the computation because of synchronization costs.
      pl - a progress logger, or null.
      Returns:
      the neighbourhood function of the specified graph as an array of longs.

    • distanceCumulativeDistributionFunction

      public static double[] distanceCumulativeDistributionFunction​(double[] neighbourhoodFunction)
      Returns the distance cumulative distribution function.
      Parameters:
      neighbourhoodFunction - a neighbourhood function or distance cumulative distribution function.
      Returns:
      the distance cumulative distribution function.

    • distanceProbabilityMassFunction

      public static double[] distanceProbabilityMassFunction​(double[] neighbourhoodFunction)
      Returns the probability mass function of the distance distribution.
      Parameters:
      neighbourhoodFunction - a neighbourhood function or distance cumulative distribution function.
      Returns:
      the probability mass function of the distance distribution.

    • effectiveDiameter

      public static double effectiveDiameter​(double alpha, double[] neighbourhoodFunction)
      Returns the effective diameter at a specified fraction.
      Parameters:
      alpha - the desired fraction of reachable pairs of nodes (usually, 0.9).
      neighbourhoodFunction - a neighbourhood function or distance cumulative distribution function.
      Returns:
      the effective diameter at fraction.

    • effectiveDiameter

      public static double effectiveDiameter​(double[] neighbourhoodFunction)
      Returns the effective diameter at 0.9.
      Parameters:
      neighbourhoodFunction - a neighbourhood function (or distance cumulative distribution function).
      Returns:
      the effective diameter at 0.9.

    • medianDistance

      public static double medianDistance​(double[] neighbourhoodFunction)
      Returns the median of distances between all pairs of nodes.
      Parameters:
      neighbourhoodFunction - a neighbourhood function.
      Returns:
      the median distance, which might be Double.POSITIVE_INFINITY if less than half of the pairs of nodes are reachable.

    • medianDistance

      public static double medianDistance​(int n, double[] neighbourhoodFunction)
      Returns the median of distances between all pairs of nodes.

      Note that if you have an actual neighbourhood function, you can safely pass its first value as first argument; however, having the number of nodes as a separate input makes it possible passing this method a distance cumulative distribution function, too.

      Parameters:
      n - the number of nodes in the graph.
      neighbourhoodFunction - a neighbourhood function (or distance cumulative distribution function).
      Returns:
      the median distance, which might be Double.POSITIVE_INFINITY if less than half of the pairs of nodes are reachable.

    • spid

      public static double spid​(double[] neighbourhoodFunction)
      Returns the spid (shortest-paths index of dispersion).
      Parameters:
      neighbourhoodFunction - a neighbourhood function (or distance cumulative distribution function).
      Returns:
      the spid.

    • averageDistance

      public static double averageDistance​(double[] neighbourhoodFunction)
      Returns the average of the distances between reachable pairs of nodes.
      Parameters:
      neighbourhoodFunction - a neighbourhood function (or distance cumulative distribution function).
      Returns:
      the average of the distances between reachable pairs of nodes.

    • harmonicDiameter

      public static double harmonicDiameter​(double[] neighbourhoodFunction)
      Returns the harmonic diameter, that is, the harmonic mean of all distances.
      Parameters:
      neighbourhoodFunction - a neighbourhood function.
      Returns:
      the harmonic diameter.

    • harmonicDiameter

      public static double harmonicDiameter​(int n, double[] neighbourhoodFunction)
      Returns the harmonic diameter, that is, the harmonic mean of all distances.

      Note that if you have an actual neighbourhood function, you can safely pass its first value as first argument; however, having the number of nodes as a separate input makes it possible passing this method a distance cumulative distribution function, too.

      Parameters:
      n - the number of nodes in the graph.
      neighbourhoodFunction - a neighbourhood function (or distance cumulative distribution function).
      Returns:
      the harmonic diameter.

    • main

      public static void main​(String[] arg) throws IOException, JSAPException
      Throws:
      IOException
      JSAPException