Package org.jgrapht

Class GraphMetrics

  • public abstract class GraphMetrics
extends java.lang.Object
    Collection of methods which provide numerical graph information.
    Author:
    Joris Kinable, Alexandru Valeanu

    • Constructor Summary

      Constructors 
      Constructor Description
      GraphMetrics()  

    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      static <V,​E>
      double      		 getDiameter​(Graph<V,​E> graph)
      Compute the diameter of the graph.
      static <V,​E>
      int      		 getGirth​(Graph<V,​E> graph)
      Compute the girth of the graph.
      static <V,​E>
      long      		 getNumberOfTriangles​(Graph<V,​E> graph)
      An $O(|E|^{3/2})$ algorithm for counting the number of non-trivial triangles in an undirected graph.
      static <V,​E>
      double      		 getRadius​(Graph<V,​E> graph)
      Compute the radius of the graph.

      • Methods inherited from class java.lang.Object

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

    • Constructor Detail

      • GraphMetrics

        public GraphMetrics()

    • Method Detail

      • getDiameter

        public static <V,​E> double getDiameter​(Graph<V,​E> graph)
        Compute the diameter of the graph. The diameter of a graph is defined as $\max_{v\in V}\epsilon(v)$, where $\epsilon(v)$ is the eccentricity of vertex $v$. In other words, this method computes the 'longest shortest path'. Two special cases exist. If the graph has no vertices, the diameter is 0. If the graph is disconnected, the diameter is Double.POSITIVE_INFINITY.

        For more fine-grained control over this method, or if you need additional distance metrics such as the graph radius, consider using GraphMeasurer instead.

        Type Parameters:
        V - graph vertex type
        E - graph edge type
        Parameters:
        graph - input graph
        Returns:
        the diameter of the graph.

      • getRadius

        public static <V,​E> double getRadius​(Graph<V,​E> graph)
        Compute the radius of the graph. The radius of a graph is defined as $\min_{v\in V}\epsilon(v)$, where $\epsilon(v)$ is the eccentricity of vertex $v$. Two special cases exist. If the graph has no vertices, the radius is 0. If the graph is disconnected, the diameter is Double.POSITIVE_INFINITY.

        For more fine-grained control over this method, or if you need additional distance metrics such as the graph diameter, consider using GraphMeasurer instead.

        Type Parameters:
        V - graph vertex type
        E - graph edge type
        Parameters:
        graph - input graph
        Returns:
        the diameter of the graph.

      • getGirth

        public static <V,​E> int getGirth​(Graph<V,​E> graph)
        Compute the girth of the graph. The girth of a graph is the length (number of edges) of the smallest cycle in the graph. Acyclic graphs are considered to have infinite girth. For directed graphs, the length of the shortest directed cycle is returned (see Bang-Jensen, J., Gutin, G., Digraphs: Theory, Algorithms and Applications, Springer Monographs in Mathematics, ch 1, ch 8.4.). Simple undirected graphs have a girth of at least 3 (triangle cycle). Directed graphs and Multigraphs have a girth of at least 2 (parallel edges/arcs), and in Pseudo graphs have a girth of at least 1 (self-loop).

        This implementation is loosely based on these notes. In essence, this method invokes a Breadth-First search from every vertex in the graph. A single Breadth-First search takes $O(n+m)$ time, where $n$ is the number of vertices in the graph, and $m$ the number of edges. Consequently, the runtime complexity of this method is $O(n(n+m))=O(mn)$.

        An algorithm with the same worst case runtime complexity, but a potentially better average runtime complexity of $O(n^2)$ is described in: Itai, A. Rodeh, M. Finding a minimum circuit in a graph. SIAM J. Comput. Vol 7, No 4, 1987.

        Type Parameters:
        V - graph vertex type
        E - graph edge type
        Parameters:
        graph - input graph
        Returns:
        girth of the graph, or Integer.MAX_VALUE if the graph is acyclic.

      • getNumberOfTriangles

        public static <V,​E> long getNumberOfTriangles​(Graph<V,​E> graph)
        An $O(|E|^{3/2})$ algorithm for counting the number of non-trivial triangles in an undirected graph. A non-trivial triangle is formed by three distinct vertices all connected to each other.

        For more details of this algorithm see Ullman, Jeffrey: "Mining of Massive Datasets", Cambridge University Press, Chapter 10

        Type Parameters:
        V - the graph vertex type
        E - the graph edge type
        Parameters:
        graph - the input graph
        Returns:
        the number of triangles in the graph
        Throws:
        java.lang.NullPointerException - if graph is null
        java.lang.IllegalArgumentException - if graph is not undirected