## Class SparseIntUndirectedGraph

• All Implemented Interfaces:
Graph<Integer,​Integer>
Direct Known Subclasses:
SparseIntUndirectedWeightedGraph

public class SparseIntUndirectedGraph
extends AbstractGraph<Integer,​Integer>
Sparse undirected graph.

Assuming the graph has $n$ vertices, the vertices are numbered from $0$ to $n-1$. Similarly, edges are numbered from $0$ to $m-1$ where $m$ is the total number of edges.

It stores the boolean incidence matrix of the graph (rows are vertices and columns are edges) as Compressed Sparse Rows (CSR). In order to also support constant time source and target lookups from an edge identifier we also store the transposed of the incidence matrix again in compressed sparse rows format. This is a classic format for write-once read-many use cases. Thus, the graph is unmodifiable.

The question of whether a sparse or dense representation is more appropriate is highly dependent on various factors such as the graph, the machine running the algorithm and the algorithm itself. Wilkinson defined a matrix as "sparse" if it has enough zeros that it pays to take advantage of them. For more details see

• Wilkinson, J. H. 1971. Linear algebra; part II: the algebraic eigenvalue problem. In Handbook for Automatic Computation, J. H. Wilkinson and C. Reinsch, Eds. Vol. 2. Springer-Verlag, Berlin, New York.
Author:
Dimitrios Michail
• ### Field Summary

Fields
Modifier and Type Field Description
protected org.jgrapht.opt.graph.sparse.CSRBooleanMatrix incidenceMatrix
protected org.jgrapht.opt.graph.sparse.CSRBooleanMatrix incidenceMatrixT
protected static String UNMODIFIABLE
• ### Fields inherited from interface org.jgrapht.Graph

DEFAULT_EDGE_WEIGHT
• ### Constructor Summary

Constructors
Constructor Description
SparseIntUndirectedGraph​(int numVertices, List<Pair<Integer,​Integer>> edges)
Create a new graph from an edge list
• ### Method Summary

All Methods
Modifier and Type Method Description
Integer addEdge​(Integer sourceVertex, Integer targetVertex)
Creates a new edge in this graph, going from the source vertex to the target vertex, and returns the created edge.
boolean addEdge​(Integer sourceVertex, Integer targetVertex, Integer e)
Adds the specified edge to this graph, going from the source vertex to the target vertex.
Integer addVertex()
Creates a new vertex in this graph and returns it.
boolean addVertex​(Integer v)
protected boolean assertEdgeExist​(Integer e)
Ensures that the specified edge exists in this graph, or else throws exception.
protected boolean assertVertexExist​(Integer v)
Ensures that the specified vertex exists in this graph, or else throws exception.
boolean containsEdge​(Integer e)
Returns true if this graph contains the specified edge.
boolean containsVertex​(Integer v)
Returns true if this graph contains the specified vertex.
int degreeOf​(Integer vertex)
Returns the degree of the specified vertex.
Set<Integer> edgeSet()
Returns a set of the edges contained in this graph.
Set<Integer> edgesOf​(Integer vertex)
Returns a set of all edges touching the specified vertex.
Set<Integer> getAllEdges​(Integer sourceVertex, Integer targetVertex)
Returns a set of all edges connecting source vertex to target vertex if such vertices exist in this graph.
Integer getEdge​(Integer sourceVertex, Integer targetVertex)
Returns an edge connecting source vertex to target vertex if such vertices and such edge exist in this graph.
Integer getEdgeSource​(Integer e)
Returns the source vertex of an edge.
Supplier<Integer> getEdgeSupplier()
Return the edge supplier that the graph uses whenever it needs to create new edges.
Integer getEdgeTarget​(Integer e)
Returns the target vertex of an edge.
double getEdgeWeight​(Integer e)
Returns the weight assigned to a given edge.
GraphType getType()
Get the graph type.
Supplier<Integer> getVertexSupplier()
Return the vertex supplier that the graph uses whenever it needs to create new vertices.
Set<Integer> incomingEdgesOf​(Integer vertex)
Returns a set of all edges incoming into the specified vertex.
int inDegreeOf​(Integer vertex)
Returns the "in degree" of the specified vertex.
int outDegreeOf​(Integer vertex)
Returns the "out degree" of the specified vertex.
Set<Integer> outgoingEdgesOf​(Integer vertex)
Returns a set of all edges outgoing from the specified vertex.
boolean removeEdge​(Integer e)
Removes the specified edge from the graph.
Integer removeEdge​(Integer sourceVertex, Integer targetVertex)
Removes an edge going from source vertex to target vertex, if such vertices and such edge exist in this graph.
boolean removeVertex​(Integer v)
Removes the specified vertex from this graph including all its touching edges if present.
void setEdgeWeight​(Integer e, double weight)
Assigns a weight to an edge.
Set<Integer> vertexSet()
Returns a set of the vertices contained in this graph.
• ### Methods inherited from class org.jgrapht.graph.AbstractGraph

containsEdge, equals, hashCode, removeAllEdges, removeAllEdges, removeAllEdges, removeAllVertices, toString, toStringFromSets
• ### Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait
• ### Methods inherited from interface org.jgrapht.Graph

setEdgeWeight
• ### Field Detail

• #### UNMODIFIABLE

protected static final String UNMODIFIABLE
Constant Field Values
• #### incidenceMatrix

protected org.jgrapht.opt.graph.sparse.CSRBooleanMatrix incidenceMatrix
• #### incidenceMatrixT

protected org.jgrapht.opt.graph.sparse.CSRBooleanMatrix incidenceMatrixT
• ### Constructor Detail

• #### SparseIntUndirectedGraph

public SparseIntUndirectedGraph​(int numVertices,
List<Pair<Integer,​Integer>> edges)
Create a new graph from an edge list
Parameters:
numVertices - number of vertices
edges - edge list
• ### Method Detail

• #### getVertexSupplier

public Supplier<Integer> getVertexSupplier()
Description copied from interface: Graph
Return the vertex supplier that the graph uses whenever it needs to create new vertices.

A graph uses the vertex supplier to create new vertex objects whenever a user calls method Graph.addVertex(). Users can also create the vertex in user code and then use method Graph.addVertex(Object) to add the vertex.

In contrast with the Supplier interface, the vertex supplier has the additional requirement that a new and distinct result is returned every time it is invoked. More specifically for a new vertex to be added in a graph v must not be equal to any other vertex in the graph. More formally, the graph must not contain any vertex v2 such that v2.equals(v).

Care must also be taken when interchanging calls to methods Graph.addVertex(Object) and Graph.addVertex(). In such a case the user must make sure never to add vertices in the graph using method Graph.addVertex(Object), which are going to be returned in the future by the supplied vertex supplier. Such a sequence will result into an IllegalArgumentException when calling method Graph.addVertex().

Returns:
the vertex supplier or null if the graph has no such supplier
• #### getEdgeSupplier

public Supplier<Integer> getEdgeSupplier()
Description copied from interface: Graph
Return the edge supplier that the graph uses whenever it needs to create new edges.

A graph uses the edge supplier to create new edge objects whenever a user calls method Graph.addEdge(Object, Object). Users can also create the edge in user code and then use method Graph.addEdge(Object, Object, Object) to add the edge.

In contrast with the Supplier interface, the edge supplier has the additional requirement that a new and distinct result is returned every time it is invoked. More specifically for a new edge to be added in a graph e must not be equal to any other edge in the graph (even if the graph allows edge-multiplicity). More formally, the graph must not contain any edge e2 such that e2.equals(e).

Returns:
the edge supplier null if the graph has no such supplier

public Integer addEdge​(Integer sourceVertex,
Integer targetVertex)
Description copied from interface: Graph
Creates a new edge in this graph, going from the source vertex to the target vertex, and returns the created edge. Some graphs do not allow edge-multiplicity. In such cases, if the graph already contains an edge from the specified source to the specified target, than this method does not change the graph and returns null.

The source and target vertices must already be contained in this graph. If they are not found in graph IllegalArgumentException is thrown.

This method creates the new edge e using this graph's edge supplier (see Graph.getEdgeSupplier()). For the new edge to be added e must not be equal to any other edge the graph (even if the graph allows edge-multiplicity). More formally, the graph must not contain any edge e2 such that e2.equals(e). If such  e2 is found then the newly created edge e is abandoned, the method leaves this graph unchanged and returns null.

If the underlying graph implementation's Graph.getEdgeSupplier() returns null, then this method cannot create edges and throws an UnsupportedOperationException.

Parameters:
sourceVertex - source vertex of the edge.
targetVertex - target vertex of the edge.
Returns:
The newly created edge if added to the graph, otherwise  null.
Graph.getEdgeSupplier()

public boolean addEdge​(Integer sourceVertex,
Integer targetVertex,
Integer e)
Description copied from interface: Graph
Adds the specified edge to this graph, going from the source vertex to the target vertex. More formally, adds the specified edge,  e, to this graph if this graph contains no edge e2 such that e2.equals(e). If this graph already contains such an edge, the call leaves this graph unchanged and returns false. Some graphs do not allow edge-multiplicity. In such cases, if the graph already contains an edge from the specified source to the specified target, than this method does not change the graph and returns  false. If the edge was added to the graph, returns  true.

The source and target vertices must already be contained in this graph. If they are not found in graph IllegalArgumentException is thrown.

Parameters:
sourceVertex - source vertex of the edge.
targetVertex - target vertex of the edge.
e - edge to be added to this graph.
Returns:
true if this graph did not already contain the specified edge.
Graph.addEdge(Object, Object), Graph.getEdgeSupplier()

public boolean addVertex​(Integer v)
Description copied from interface: Graph
Adds the specified vertex to this graph if not already present. More formally, adds the specified vertex, v, to this graph if this graph contains no vertex u such that  u.equals(v). If this graph already contains such vertex, the call leaves this graph unchanged and returns false. In combination with the restriction on constructors, this ensures that graphs never contain duplicate vertices.
Parameters:
v - vertex to be added to this graph.
Returns:
true if this graph did not already contain the specified vertex.
• #### containsEdge

public boolean containsEdge​(Integer e)
Description copied from interface: Graph
Returns true if this graph contains the specified edge. More formally, returns true if and only if this graph contains an edge e2 such that e.equals(e2). If the specified edge is null returns false.
Parameters:
e - edge whose presence in this graph is to be tested.
Returns:
true if this graph contains the specified edge.
• #### containsVertex

public boolean containsVertex​(Integer v)
Description copied from interface: Graph
Returns true if this graph contains the specified vertex. More formally, returns true if and only if this graph contains a vertex u such that u.equals(v). If the specified vertex is null returns false.
Parameters:
v - vertex whose presence in this graph is to be tested.
Returns:
true if this graph contains the specified vertex.
• #### edgeSet

public Set<Integer> edgeSet()
Description copied from interface: Graph
Returns a set of the edges contained in this graph. The set is backed by the graph, so changes to the graph are reflected in the set. If the graph is modified while an iteration over the set is in progress, the results of the iteration are undefined.

The graph implementation may maintain a particular set ordering (e.g. via LinkedHashSet) for deterministic iteration, but this is not required. It is the responsibility of callers who rely on this behavior to only use graph implementations which support it.

Returns:
a set of the edges contained in this graph.
• #### degreeOf

public int degreeOf​(Integer vertex)
Description copied from interface: Graph
Returns the degree of the specified vertex.

A degree of a vertex in an undirected graph is the number of edges touching that vertex. Edges with same source and target vertices (self-loops) are counted twice.

In directed graphs this method returns the sum of the "in degree" and the "out degree".

Parameters:
vertex - vertex whose degree is to be calculated.
Returns:
the degree of the specified vertex.
• #### edgesOf

public Set<Integer> edgesOf​(Integer vertex)
Description copied from interface: Graph
Returns a set of all edges touching the specified vertex. If no edges are touching the specified vertex returns an empty set.
Parameters:
vertex - the vertex for which a set of touching edges is to be returned.
Returns:
a set of all edges touching the specified vertex.
• #### inDegreeOf

public int inDegreeOf​(Integer vertex)
Description copied from interface: Graph
Returns the "in degree" of the specified vertex.

The "in degree" of a vertex in a directed graph is the number of inward directed edges from that vertex. See http://mathworld.wolfram.com/Indegree.html.

In the case of undirected graphs this method returns the number of edges touching the vertex. Edges with same source and target vertices (self-loops) are counted twice.

Parameters:
vertex - vertex whose degree is to be calculated.
Returns:
the degree of the specified vertex.
• #### incomingEdgesOf

public Set<Integer> incomingEdgesOf​(Integer vertex)
Description copied from interface: Graph
Returns a set of all edges incoming into the specified vertex.

In the case of undirected graphs this method returns all edges touching the vertex, thus, some of the returned edges may have their source and target vertices in the opposite order.

Parameters:
vertex - the vertex for which the list of incoming edges to be returned.
Returns:
a set of all edges incoming into the specified vertex.
• #### outDegreeOf

public int outDegreeOf​(Integer vertex)
Description copied from interface: Graph
Returns the "out degree" of the specified vertex.

The "out degree" of a vertex in a directed graph is the number of outward directed edges from that vertex. See http://mathworld.wolfram.com/Outdegree.html.

In the case of undirected graphs this method returns the number of edges touching the vertex. Edges with same source and target vertices (self-loops) are counted twice.

Parameters:
vertex - vertex whose degree is to be calculated.
Returns:
the degree of the specified vertex.
• #### outgoingEdgesOf

public Set<Integer> outgoingEdgesOf​(Integer vertex)
Description copied from interface: Graph
Returns a set of all edges outgoing from the specified vertex.

In the case of undirected graphs this method returns all edges touching the vertex, thus, some of the returned edges may have their source and target vertices in the opposite order.

Parameters:
vertex - the vertex for which the list of outgoing edges to be returned.
Returns:
a set of all edges outgoing from the specified vertex.
• #### removeEdge

public Integer removeEdge​(Integer sourceVertex,
Integer targetVertex)
Description copied from interface: Graph
Removes an edge going from source vertex to target vertex, if such vertices and such edge exist in this graph. Returns the edge if removed or null otherwise.
Parameters:
sourceVertex - source vertex of the edge.
targetVertex - target vertex of the edge.
Returns:
The removed edge, or null if no edge removed.
• #### removeEdge

public boolean removeEdge​(Integer e)
Description copied from interface: Graph
Removes the specified edge from the graph. Removes the specified edge from this graph if it is present. More formally, removes an edge  e2 such that e2.equals(e), if the graph contains such edge. Returns true if the graph contained the specified edge. (The graph will not contain the specified edge once the call returns).

If the specified edge is null returns  false.

Parameters:
e - edge to be removed from this graph, if present.
Returns:
true if and only if the graph contained the specified edge.
• #### removeVertex

public boolean removeVertex​(Integer v)
Description copied from interface: Graph
Removes the specified vertex from this graph including all its touching edges if present. More formally, if the graph contains a vertex  u such that u.equals(v), the call removes all edges that touch u and then removes u itself. If no such u is found, the call leaves the graph unchanged. Returns true if the graph contained the specified vertex. (The graph will not contain the specified vertex once the call returns).

If the specified vertex is null returns  false.

Parameters:
v - vertex to be removed from this graph, if present.
Returns:
true if the graph contained the specified vertex; false otherwise.
• #### vertexSet

public Set<Integer> vertexSet()
Description copied from interface: Graph
Returns a set of the vertices contained in this graph. The set is backed by the graph, so changes to the graph are reflected in the set. If the graph is modified while an iteration over the set is in progress, the results of the iteration are undefined.

The graph implementation may maintain a particular set ordering (e.g. via LinkedHashSet) for deterministic iteration, but this is not required. It is the responsibility of callers who rely on this behavior to only use graph implementations which support it.

Returns:
a set view of the vertices contained in this graph.
• #### getType

public GraphType getType()
Description copied from interface: Graph
Get the graph type. The graph type can be used to query for additional metadata such as whether the graph supports directed or undirected edges, self-loops, multiple (parallel) edges, weights, etc.
Returns:
the graph type
• #### getEdgeWeight

public double getEdgeWeight​(Integer e)
Description copied from interface: Graph
Returns the weight assigned to a given edge. Unweighted graphs return 1.0 (as defined by Graph.DEFAULT_EDGE_WEIGHT), allowing weighted-graph algorithms to apply to them when meaningful.
Parameters:
e - edge of interest
Returns:
edge weight
• #### setEdgeWeight

public void setEdgeWeight​(Integer e,
double weight)
Description copied from interface: Graph
Assigns a weight to an edge.
Parameters:
e - edge on which to set weight
weight - new weight for edge
• #### getEdgeSource

public Integer getEdgeSource​(Integer e)
Description copied from interface: Graph
Returns the source vertex of an edge. For an undirected graph, source and target are distinguishable designations (but without any mathematical meaning).
Parameters:
e - edge of interest
Returns:
source vertex
• #### getEdgeTarget

public Integer getEdgeTarget​(Integer e)
Description copied from interface: Graph
Returns the target vertex of an edge. For an undirected graph, source and target are distinguishable designations (but without any mathematical meaning).
Parameters:
e - edge of interest
Returns:
target vertex
• #### getEdge

public Integer getEdge​(Integer sourceVertex,
Integer targetVertex)
Returns an edge connecting source vertex to target vertex if such vertices and such edge exist in this graph. Otherwise returns  null. If any of the specified vertices is null returns null

In undirected graphs, the returned edge may have its source and target vertices in the opposite order.

This operation costs $O(d)$ where $d$ is the degree of the source vertex.
Parameters:
sourceVertex - source vertex of the edge.
targetVertex - target vertex of the edge.
Returns:
an edge connecting source vertex to target vertex.
• #### getAllEdges

public Set<Integer> getAllEdges​(Integer sourceVertex,
Integer targetVertex)
Returns a set of all edges connecting source vertex to target vertex if such vertices exist in this graph. If any of the vertices does not exist or is null, returns null. If both vertices exist but no edges found, returns an empty set.

In undirected graphs, some of the returned edges may have their source and target vertices in the opposite order. In simple graphs the returned set is either singleton set or empty set.

This operation costs $O(d)$ where $d$ is the degree of the source vertex.
Parameters:
sourceVertex - source vertex of the edge.
targetVertex - target vertex of the edge.
Returns:
a set of all edges connecting source vertex to target vertex.
• #### assertVertexExist

protected boolean assertVertexExist​(Integer v)
Ensures that the specified vertex exists in this graph, or else throws exception.
Overrides:
assertVertexExist in class AbstractGraph<Integer,​Integer>
Parameters:
v - vertex
Returns:
true if this assertion holds.
Throws:
IllegalArgumentException - if specified vertex does not exist in this graph.
• #### assertEdgeExist

protected boolean assertEdgeExist​(Integer e)
Ensures that the specified edge exists in this graph, or else throws exception.
Parameters:
e - edge
Returns:
true if this assertion holds.
Throws:
IllegalArgumentException - if specified edge does not exist in this graph.