Package it.unimi.dsi.webgraph.algo

Class BetweennessCentrality

java.lang.Object
it.unimi.dsi.webgraph.algo.BetweennessCentrality
public class BetweennessCentrality
extends Object
Computes the betweenness centrality using an implementation of Brandes's algorithm (Ulrik Brandes, “A Faster Algorithm for Betweenness Centrality”, Journal of Mathematical Sociology 25(2):163−177, 2001) that uses multiple parallel breadth-first visits.

To use this class you first create an instance, and then invoke compute(). After that, you can peek at the field betweenness to discover the betweenness of each node.

For every three distinct nodes s, t and v, let σst be the number of shortest paths from s to t, and σst(v) the number of such paths on which v lies. The betweenness centrality of node v is defined to be the sum of δst(v)=σst(v) / σst over all pairs of distinct nodes s, t different from v (the summand is assumed to be zero whenever the denominator is zero).

Brandes's approach consists in performing a breadth-first visit from every node, recording the distance of the node from the current source. After each visit, nodes are considered in decreasing order of distance, and for each of them we consider the arcs (v,w) such that the distance of w is exactly one plus the distance of v: in this case we say that v is a parent of w. Such parents are used to compute the values of δ (exactly as in the original algorithm, but without any need to keep an explicit set of parents, which is important since this class is memory intensive).

Every visit is independent and is carried out by a separate thread. The only contention point is the update of the array accumulating the betweenness score, which is negligible. The downside is that running on k cores requires approximately k times the memory of the sequential algorithm, as only the graph and the betweenness array will be shared.

This class keeps carefully track of overflows in path counters, and will throw an exception in case they happen. Thanks to David Gleich for making me note this serious problem, which is often overlooked.

  • Field Details

    • nextNode

      protected final AtomicInteger nextNode
      The next node to be visited.

    • stop

      protected volatile boolean stop
      Whether to stop abruptly the visiting process.

    • betweenness

      public final double[] betweenness
      The array of betweenness value.

  • Constructor Details

    • BetweennessCentrality

      public BetweennessCentrality​(ImmutableGraph graph, int requestedThreads, ProgressLogger pl)
      Creates a new class for computing betweenness centrality.
      Parameters:
      graph - a graph.
      requestedThreads - the requested number of threads (0 for Runtime.availableProcessors()).
      pl - a progress logger, or null.

    • BetweennessCentrality

      public BetweennessCentrality​(ImmutableGraph graph, ProgressLogger pl)
      Creates a new class for computing betweenness centrality, using as many threads as the number of available processors.
      Parameters:
      graph - a graph.
      pl - a progress logger, or null.

    • BetweennessCentrality

      public BetweennessCentrality​(ImmutableGraph graph, int requestedThreads)
      Creates a new class for computing betweenness centrality.
      Parameters:
      graph - a graph.
      requestedThreads - the requested number of threads (0 for Runtime.availableProcessors()).

    • BetweennessCentrality

      public BetweennessCentrality​(ImmutableGraph graph)
      Creates a new class for computing betweenness centrality, using as many threads as the number of available processors.
      Parameters:
      graph - a graph.

  • Method Details