org.jgrapht

## Class GraphTests

• public abstract class GraphTests
extends Object
A collection of utilities to test for various graph properties.
Author:
Barak Naveh, Dimitrios Michail, Joris Kinable, Alexandru Valeanu
• ### Constructor Summary

Constructors
Constructor and Description
GraphTests()
• ### Method Summary

All Methods
Modifier and Type Method and Description
static <V,E> boolean hasMultipleEdges(Graph<V,E> graph)
Check if a graph has multiple edges (parallel edges), that is, whether the graph contains two or more edges connecting the same pair of vertices.
static <V,E> boolean hasOreProperty(Graph<V,E> graph)
Tests whether an undirected graph meets Ore's condition to be Hamiltonian.
static <V,E> boolean hasSelfLoops(Graph<V,E> graph)
Check if a graph has self-loops.
static <V,E> boolean isBiconnected(Graph<V,E> graph)
Tests if the inspected graph is biconnected.
static <V,E> boolean isBipartite(Graph<V,E> graph)
Test whether a graph is bipartite.
static <V,E> boolean isBipartitePartition(Graph<V,E> graph, Set<? extends V> firstPartition, Set<? extends V> secondPartition)
Test whether a partition of the vertices into two sets is a bipartite partition.
static <V,E> boolean isChordal(Graph<V,E> graph)
Checks whether a graph is chordal.
static <V,E> boolean isComplete(Graph<V,E> graph)
Test whether a graph is complete.
static <V,E> boolean isConnected(Graph<V,E> graph)
Test if the inspected graph is connected.
static <V,E> boolean isCubic(Graph<V,E> graph)
Tests whether a graph is cubic.
static <V,E> boolean isEmpty(Graph<V,E> graph)
Test whether a graph is empty.
static <V,E> boolean isEulerian(Graph<V,E> graph)
Test whether a graph is Eulerian.
static <V,E> boolean isForest(Graph<V,E> graph)
Test whether an undirected graph is a forest.
static <V,E> boolean isOverfull(Graph<V,E> graph)
Test whether a graph is overfull.
static <V,E> boolean isPerfect(Graph<V,E> graph)
Checks that the specified graph is perfect.
static <V,E> boolean isSimple(Graph<V,E> graph)
Check if a graph is simple.
static <V,E> boolean isSplit(Graph<V,E> graph)
Test whether an undirected graph is a split graph.
static <V,E> boolean isStronglyConnected(Graph<V,E> graph)
Test whether a graph is strongly connected.
static <V,E> boolean isTree(Graph<V,E> graph)
Test whether an undirected graph is a tree.
static <V,E> boolean isTriangleFree(Graph<V,E> graph)
Tests whether an undirected graph is triangle-free (i.e.
static <V,E> boolean isWeaklyChordal(Graph<V,E> graph)
Checks whether a graph is weakly chordal.
static <V,E> boolean isWeaklyConnected(Graph<V,E> graph)
Test whether a directed graph is weakly connected.
static <V,E> Graph<V,E> requireDirected(Graph<V,E> graph)
Checks that the specified graph is directed and throws an IllegalArgumentException if it is not.
static <V,E> Graph<V,E> requireDirected(Graph<V,E> graph, String message)
Checks that the specified graph is directed and throws a customized IllegalArgumentException if it is not.
static <V,E> Graph<V,E> requireDirectedOrUndirected(Graph<V,E> graph)
Checks that the specified graph is directed and throws an IllegalArgumentException if it is not.
static <V,E> Graph<V,E> requireDirectedOrUndirected(Graph<V,E> graph, String message)
Checks that the specified graph is directed or undirected and throws a customized IllegalArgumentException if it is not.
static <V,E> Graph<V,E> requireUndirected(Graph<V,E> graph)
Checks that the specified graph is undirected and throws an IllegalArgumentException if it is not.
static <V,E> Graph<V,E> requireUndirected(Graph<V,E> graph, String message)
Checks that the specified graph is undirected and throws a customized IllegalArgumentException if it is not.
static <V,E> Graph<V,E> requireWeighted(Graph<V,E> graph)
Checks that the specified graph is weighted and throws a customized IllegalArgumentException if it is not.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### GraphTests

public GraphTests()
• ### Method Detail

• #### isEmpty

public static <V,E> boolean isEmpty(Graph<V,E> graph)
Test whether a graph is empty. An empty graph on n nodes consists of n isolated vertices with no edges.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
Returns:
true if the graph is empty, false otherwise
• #### isSimple

public static <V,E> boolean isSimple(Graph<V,E> graph)
Check if a graph is simple. A graph is simple if it has no self-loops and multiple (parallel) edges.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - a graph
Returns:
true if a graph is simple, false otherwise
• #### hasSelfLoops

public static <V,E> boolean hasSelfLoops(Graph<V,E> graph)
Check if a graph has self-loops. A self-loop is an edge with the same source and target vertices.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - a graph
Returns:
true if a graph has self-loops, false otherwise
• #### hasMultipleEdges

public static <V,E> boolean hasMultipleEdges(Graph<V,E> graph)
Check if a graph has multiple edges (parallel edges), that is, whether the graph contains two or more edges connecting the same pair of vertices.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - a graph
Returns:
true if a graph has multiple edges, false otherwise
• #### isComplete

public static <V,E> boolean isComplete(Graph<V,E> graph)
Test whether a graph is complete. A complete undirected graph is a simple graph in which every pair of distinct vertices is connected by a unique edge. A complete directed graph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges (one in each direction).
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
Returns:
true if the graph is complete, false otherwise
• #### isConnected

public static <V,E> boolean isConnected(Graph<V,E> graph)
Test if the inspected graph is connected. A graph is connected when, while ignoring edge directionality, there exists a path between every pair of vertices. In a connected graph, there are no unreachable vertices. When the inspected graph is a directed graph, this method returns true if and only if the inspected graph is weakly connected. An empty graph is not considered connected.

This method does not performing any caching, instead recomputes everything from scratch. In case more control is required use ConnectivityInspector directly.

Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
Returns:
true if the graph is connected, false otherwise
ConnectivityInspector
• #### isBiconnected

public static <V,E> boolean isBiconnected(Graph<V,E> graph)
Tests if the inspected graph is biconnected. A biconnected graph is a connected graph on two or more vertices having no cutpoints.

This method does not performing any caching, instead recomputes everything from scratch. In case more control is required use BiconnectivityInspector directly.

Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
Returns:
true if the graph is biconnected, false otherwise
BiconnectivityInspector
• #### isWeaklyConnected

public static <V,E> boolean isWeaklyConnected(Graph<V,E> graph)
Test whether a directed graph is weakly connected.

This method does not performing any caching, instead recomputes everything from scratch. In case more control is required use ConnectivityInspector directly.

Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
Returns:
true if the graph is weakly connected, false otherwise
ConnectivityInspector
• #### isStronglyConnected

public static <V,E> boolean isStronglyConnected(Graph<V,E> graph)
Test whether a graph is strongly connected.

This method does not performing any caching, instead recomputes everything from scratch. In case more control is required use KosarajuStrongConnectivityInspector directly.

In case of undirected graphs this method delegated to isConnected(Graph).

Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
Returns:
true if the graph is strongly connected, false otherwise
KosarajuStrongConnectivityInspector
• #### isTree

public static <V,E> boolean isTree(Graph<V,E> graph)
Test whether an undirected graph is a tree.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
Returns:
true if the graph is tree, false otherwise
• #### isForest

public static <V,E> boolean isForest(Graph<V,E> graph)
Test whether an undirected graph is a forest. A forest is a set of disjoint trees. By definition, any acyclic graph is a forest. This includes the empty graph and the class of tree graphs.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
Returns:
true if the graph is forest, false otherwise
• #### isOverfull

public static <V,E> boolean isOverfull(Graph<V,E> graph)
Test whether a graph is overfull. A graph is overfull if $|E|>\Delta(G)\lfloor |V|/2 \rfloor$, where $\Delta(G)$ is the maximum degree of the graph.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
Returns:
true if the graph is overfull, false otherwise
• #### isSplit

public static <V,E> boolean isSplit(Graph<V,E> graph)
Test whether an undirected graph is a split graph. A split graph is a graph in which the vertices can be partitioned into a clique and an independent set. Split graphs are a special class of chordal graphs. Given the degree sequence $d_1 \geq,\dots,\geq d_n$ of $G$, a graph is a split graph if and only if : $\sum_{i=1}^m d_i = m (m - 1) + \sum_{i=m + 1}^nd_i$, where $m = \max_i \{d_i\geq i-1\}$. If the graph is a split graph, then the $m$ vertices with the largest degrees form a maximum clique in $G$, and the remaining vertices constitute an independent set. See Brandstadt, A., Le, V., Spinrad, J. Graph Classes: A Survey. Philadelphia, PA: SIAM, 1999. for details.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
Returns:
true if the graph is a split graph, false otherwise
• #### isBipartite

public static <V,E> boolean isBipartite(Graph<V,E> graph)
Test whether a graph is bipartite.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
Returns:
true if the graph is bipartite, false otherwise
BipartitePartitioning.isBipartite()
• #### isBipartitePartition

public static <V,E> boolean isBipartitePartition(Graph<V,E> graph,
Set<? extends V> firstPartition,
Set<? extends V> secondPartition)
Test whether a partition of the vertices into two sets is a bipartite partition.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
firstPartition - the first vertices partition
secondPartition - the second vertices partition
Returns:
true if the partition is a bipartite partition, false otherwise
BipartitePartitioning.isValidPartitioning(PartitioningAlgorithm.Partitioning)
• #### isCubic

public static <V,E> boolean isCubic(Graph<V,E> graph)
Tests whether a graph is cubic. A graph is cubic if all vertices have degree 3.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
Returns:
true if the graph is cubic, false otherwise
• #### isEulerian

public static <V,E> boolean isEulerian(Graph<V,E> graph)
Test whether a graph is Eulerian. An undirected graph is Eulerian if it is connected and each vertex has an even degree. A directed graph is Eulerian if it is strongly connected and each vertex has the same incoming and outgoing degree. Test whether a graph is Eulerian. An Eulerian graph is a graph containing an Eulerian cycle.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
Returns:
true if the graph is Eulerian, false otherwise
HierholzerEulerianCycle.isEulerian(Graph)
• #### isChordal

public static <V,E> boolean isChordal(Graph<V,E> graph)
Checks whether a graph is chordal. A chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
Returns:
true if the graph is chordal, false otherwise
ChordalityInspector.isChordal()
• #### isWeaklyChordal

public static <V,E> boolean isWeaklyChordal(Graph<V,E> graph)
Checks whether a graph is weakly chordal.

The following definitions are equivalent:

1. A graph is weakly chordal (weakly triangulated) if neither it nor its complement contains a chordless cycles with five or more vertices.
2. A 2-pair in a graph is a pair of non-adjacent vertices $x$, $y$ such that every chordless path has exactly two edges. A graph is weakly chordal if every connected induced subgraph $H$ that is not a complete graph, contains a 2-pair.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
Returns:
true if the graph is weakly chordal, false otherwise
WeakChordalityInspector.isWeaklyChordal()
• #### hasOreProperty

public static <V,E> boolean hasOreProperty(Graph<V,E> graph)
Tests whether an undirected graph meets Ore's condition to be Hamiltonian. Let $G$ be a (finite and simple) graph with $n \geq 3$ vertices. We denote by $deg(v)$ the degree of a vertex $v$ in $G$, i.e. the number of incident edges in $G$ to $v$. Then, Ore's theorem states that if $deg(v) + deg(w) \geq n$ for every pair of distinct non-adjacent vertices $v$ and $w$ of $G$, then $G$ is Hamiltonian.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
Returns:
true if the graph meets Ore's condition, false otherwise
PalmerHamiltonianCycle
• #### isTriangleFree

public static <V,E> boolean isTriangleFree(Graph<V,E> graph)
Tests whether an undirected graph is triangle-free (i.e. no three distinct vertices form a triangle of edges). The implementation of this method uses GraphMetrics.getNumberOfTriangles(Graph).
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the input graph
Returns:
true if the graph is triangle-free, false otherwise
• #### isPerfect

public static <V,E> boolean isPerfect(Graph<V,E> graph)
Checks that the specified graph is perfect. Due to the Strong Perfect Graph Theorem Berge Graphs are the same as perfect Graphs. The implementation of this method is delegated to BergeGraphInspector
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the graph reference to check for being perfect or not
Returns:
true if the graph is perfect, false otherwise
• #### requireDirected

public static <V,E> Graph<V,E> requireDirected(Graph<V,E> graph,
String message)
Checks that the specified graph is directed and throws a customized IllegalArgumentException if it is not. Also checks that the graph reference is not null and throws a NullPointerException if it is.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the graph reference to check for beeing directed and not null
message - detail message to be used in the event that an exception is thrown
Returns:
graph if directed and not null
Throws:
NullPointerException - if graph is null
IllegalArgumentException - if graph is not directed
• #### requireDirected

public static <V,E> Graph<V,E> requireDirected(Graph<V,E> graph)
Checks that the specified graph is directed and throws an IllegalArgumentException if it is not. Also checks that the graph reference is not null and throws a NullPointerException if it is.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the graph reference to check for beeing directed and not null
Returns:
graph if directed and not null
Throws:
NullPointerException - if graph is null
IllegalArgumentException - if graph is not directed
• #### requireUndirected

public static <V,E> Graph<V,E> requireUndirected(Graph<V,E> graph,
String message)
Checks that the specified graph is undirected and throws a customized IllegalArgumentException if it is not. Also checks that the graph reference is not null and throws a NullPointerException if it is.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the graph reference to check for being undirected and not null
message - detail message to be used in the event that an exception is thrown
Returns:
graph if undirected and not null
Throws:
NullPointerException - if graph is null
IllegalArgumentException - if graph is not undirected
• #### requireUndirected

public static <V,E> Graph<V,E> requireUndirected(Graph<V,E> graph)
Checks that the specified graph is undirected and throws an IllegalArgumentException if it is not. Also checks that the graph reference is not null and throws a NullPointerException if it is.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the graph reference to check for being undirected and not null
Returns:
graph if undirected and not null
Throws:
NullPointerException - if graph is null
IllegalArgumentException - if graph is not undirected
• #### requireDirectedOrUndirected

public static <V,E> Graph<V,E> requireDirectedOrUndirected(Graph<V,E> graph,
String message)
Checks that the specified graph is directed or undirected and throws a customized IllegalArgumentException if it is not. Also checks that the graph reference is not null and throws a NullPointerException if it is.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the graph reference to check for beeing directed or undirected and not null
message - detail message to be used in the event that an exception is thrown
Returns:
graph if directed and not null
Throws:
NullPointerException - if graph is null
IllegalArgumentException - if graph is mixed
• #### requireDirectedOrUndirected

public static <V,E> Graph<V,E> requireDirectedOrUndirected(Graph<V,E> graph)
Checks that the specified graph is directed and throws an IllegalArgumentException if it is not. Also checks that the graph reference is not null and throws a NullPointerException if it is.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the graph reference to check for beeing directed and not null
Returns:
graph if directed and not null
Throws:
NullPointerException - if graph is null
IllegalArgumentException - if graph is mixed
• #### requireWeighted

public static <V,E> Graph<V,E> requireWeighted(Graph<V,E> graph)
Checks that the specified graph is weighted and throws a customized IllegalArgumentException if it is not. Also checks that the graph reference is not null and throws a NullPointerException if it is.
Type Parameters:
V - the graph vertex type
E - the graph edge type
Parameters:
graph - the graph reference to check for being weighted and not null
Returns:
graph if directed and not null
Throws:
NullPointerException - if graph is null
IllegalArgumentException - if graph is not weighted