Graph

All Known Implementing Classes:

AdjacencyMapGraph
```
public interface Graph<V,E>
```
An interface for a graph structure. A graph can be declared as either directed or undirected. In the case of an undirected graph, methods outgoingEdges and incomingEdges return the same collection, and outDegree and inDegree return the same value. Every vertex stores an element of type V (possibly null). Every edge stores an element of type E (possibly null).

Method Summary

Methods
Modifier and Type	Method and Description
`Iterable<Edge<E>>`	`edges()` Returns the edges of the graph as an iterable collection
`Vertex<V>[]`	`endVertices(Edge<E> e)` Returns the vertices of edge e as an array of length two.
`Edge<E>`	`getEdge(Vertex<V> u, Vertex<V> v)` Returns the edge from u to v, or null if they are not adjacent.
`Iterable<Edge<E>>`	`incomingEdges(Vertex<V> v)` Returns an iterable collection of edges for which vertex v is the destination.
`int`	`inDegree(Vertex<V> v)` Returns the number of edges for which vertex v is the destination.
`Edge<E>`	`insertEdge(Vertex<V> u, Vertex<V> v, E element)` Inserts and returns a new edge between vertices u and v, storing given element.
`Vertex<V>`	`insertVertex(V element)` Inserts and returns a new vertex with the given element.
`int`	`numEdges()` Returns the number of edges of the graph
`int`	`numVertices()` Returns the number of vertices of the graph
`Vertex<V>`	`opposite(Vertex<V> v, Edge<E> e)` Returns the vertex that is opposite vertex v on edge e.
`int`	`outDegree(Vertex<V> v)` Returns the number of edges leaving vertex v.
`Iterable<Edge<E>>`	`outgoingEdges(Vertex<V> v)` Returns an iterable collection of edges for which vertex v is the origin.
`void`	`removeEdge(Edge<E> e)` Removes an edge from the graph.
`void`	`removeVertex(Vertex<V> v)` Removes a vertex and all its incident edges from the graph.
`Iterable<Vertex<V>>`	`vertices()` Returns the vertices of the graph as an iterable collection

- Method Detail
  - numVertices
```
int numVertices()
```
    Returns the number of vertices of the graph
  - numEdges
```
int numEdges()
```
    Returns the number of edges of the graph
  - vertices
```
Iterable<Vertex<V>> vertices()
```
    Returns the vertices of the graph as an iterable collection
  - edges
```
Iterable<Edge<E>> edges()
```
    Returns the edges of the graph as an iterable collection
  - outDegree
```
int outDegree(Vertex<V> v)
              throws IllegalArgumentException
```
    Returns the number of edges leaving vertex v. Note that for an undirected graph, this is the same result returned by inDegree
    
    Throws:
    
    IllegalArgumentException - if v is not a valid vertex
  - inDegree
```
int inDegree(Vertex<V> v)
             throws IllegalArgumentException
```
    Returns the number of edges for which vertex v is the destination. Note that for an undirected graph, this is the same result returned by outDegree
    
    Throws:
    
    IllegalArgumentException - if v is not a valid vertex
  - outgoingEdges
```
Iterable<Edge<E>> outgoingEdges(Vertex<V> v)
                                throws IllegalArgumentException
```
    Returns an iterable collection of edges for which vertex v is the origin. Note that for an undirected graph, this is the same result returned by incomingEdges.
    
    Throws:
    
    IllegalArgumentException - if v is not a valid vertex
  - incomingEdges
```
Iterable<Edge<E>> incomingEdges(Vertex<V> v)
                                throws IllegalArgumentException
```
    Returns an iterable collection of edges for which vertex v is the destination. Note that for an undirected graph, this is the same result returned by outgoingEdges.
    
    Throws:
    
    IllegalArgumentException - if v is not a valid vertex
  - getEdge
```
Edge<E> getEdge(Vertex<V> u,
              Vertex<V> v)
                throws IllegalArgumentException
```
    Returns the edge from u to v, or null if they are not adjacent.
    
    Throws:
    
    IllegalArgumentException
  - endVertices
```
Vertex<V>[] endVertices(Edge<E> e)
                        throws IllegalArgumentException
```
    Returns the vertices of edge e as an array of length two. If the graph is directed, the first vertex is the origin, and the second is the destination. If the graph is undirected, the order is arbitrary.
    
    Throws:
    
    IllegalArgumentException
  - opposite
```
Vertex<V> opposite(Vertex<V> v,
                 Edge<E> e)
                   throws IllegalArgumentException
```
    Returns the vertex that is opposite vertex v on edge e.
    
    Throws:
    
    IllegalArgumentException
  - insertVertex
```
Vertex<V> insertVertex(V element)
```
    Inserts and returns a new vertex with the given element.
  - insertEdge
```
Edge<E> insertEdge(Vertex<V> u,
                 Vertex<V> v,
                 E element)
                   throws IllegalArgumentException
```
    Inserts and returns a new edge between vertices u and v, storing given element.
    
    Throws:
    
    IllegalArgumentException - if u or v are invalid vertices, or if an edge already exists between u and v.
  - removeVertex
```
void removeVertex(Vertex<V> v)
                  throws IllegalArgumentException
```
    Removes a vertex and all its incident edges from the graph.
    
    Throws:
    
    IllegalArgumentException
  - removeEdge
```
void removeEdge(Edge<E> e)
                throws IllegalArgumentException
```
    Removes an edge from the graph.
    
    Throws:
    
    IllegalArgumentException

Interface Graph<V,E>

Method Summary

Method Detail

numVertices

numEdges

vertices

edges

outDegree

inDegree

outgoingEdges

incomingEdges

getEdge

endVertices

opposite

insertVertex

insertEdge

removeVertex

removeEdge