## structure5 Interface Graph<V,E>

All Superinterfaces:
Iterable<V>, Structure<V>
All Known Implementing Classes:
GraphList, GraphListDirected, GraphListUndirected, GraphMatrix, GraphMatrixDirected, GraphMatrixUndirected

`public interface Graph<V,E>extends Structure<V>`

The interface describing all Graph objects. Graphs are collections of vertices connected by a set of edges. Edges may or may not be directed. Portions of the graph may be marked visited to support iterative algorithms. Iteration is provided over vertices, edges, and vertices adjacent to a particular vertex

Example usage:

To visit all of the vertices reachable from a given vertex we could use the following:

```   static void reachableFrom(`Graph` g, Object vertexLabel)
{
g.`visit(vertexLabel)`;       // visit this vertex

// recursively visit unvisited neighbor vertices
Iterator ni = g.`neighbors(vertexLabel)`;
while (ni.hasNext())
{
Object neighbor = ni.next(); // adjacent node label
if (!g.`isVisited(neighbor)`x)
{
reachableFrom(g,neighbor); // depth-first search
}
}
}
```

`structure.GraphList`, `structure.GraphMatrix`

Method Summary
` void` `add(V label)`
Add a vertex to the graph
` void` ```addEdge(V vtx1, V vtx2, E label)```
Add an edge between two vertices within the graph.
` void` `clear()`
Remove all vertices (and thus, edges) of the graph.
` boolean` `contains(V label)`
Test for vertex membership.
` boolean` ```containsEdge(V vLabel1, V vLabel2)```
Test for edge membership.
` int` `degree(V label)`
Determine out degree of vertex.
` int` `edgeCount()`
Determine the number of edges in graph.
` Iterator<Edge<V,E>>` `edges()`
Construct an iterator over all edges.
` V` `get(V label)`
Get reference to actual label of vertex.
` Edge<V,E>` ```getEdge(V label1, V label2)```
Get reference to actual edge.
` boolean` `isDirected()`
Determine if graph is directed.
` boolean` `isEmpty()`
Determine if graph is empty.
` boolean` `isVisited(V label)`
Return visited flag of vertex.
` boolean` `isVisitedEdge(Edge<V,E> e)`
Return visited flag of edge.
` Iterator<V>` `iterator()`
Construct vertex iterator.
` Iterator<V>` `neighbors(V label)`
` V` `remove(V label)`
Remove a vertex from the graph.
` E` ```removeEdge(V vLabel1, V vLabel2)```
Remove possible edge between vertices labeled vLabel1 and vLabel2.
` void` `reset()`
Clear visited flags of edges and vertices.
` int` `size()`
Determine number of vertices within graph.
` boolean` `visit(V label)`
Test and set visited flag of vertex
` boolean` `visitEdge(Edge<V,E> e)`
Test and set visited flag of edge.

Methods inherited from interface structure5.Structure
`elements, values`

Method Detail

`void add(V label)`
Add a vertex to the graph

Specified by:
`add` in interface `Structure<V>`
Parameters:
`label` - Label of the vertex; should be non-null

```void addEdge(V vtx1,
V vtx2,
E label)```
Add an edge between two vertices within the graph. Edge is directed iff graph is directed. Duplicate edges are silently replaced. Labels on edges may be null.

Parameters:
`vtx1` - First (or source, if directed) vertex.
`vtx2` - Second (or destination, if directed) vertex.
`label` - Label associated with the edge.

### remove

`V remove(V label)`
Remove a vertex from the graph. Associated edges are also removed. Non-vertices are silently ignored.

Specified by:
`remove` in interface `Structure<V>`
Parameters:
`label` - The label of the vertex within the graph.
Returns:
The label associated with the vertex.

### removeEdge

```E removeEdge(V vLabel1,
V vLabel2)```
Remove possible edge between vertices labeled vLabel1 and vLabel2. Directed edges consider vLabel1 to be the source.

Parameters:
`vLabel1` - First (or source, if directed) vertex.
`vLabel2` - Second (or destination, if directed) vertex.
Returns:
The label associated with the edge removed.

### get

`V get(V label)`
Get reference to actual label of vertex. Vertex labels are matched using their equals method, which may or may not test for actual equivalence. Result remains part of graph.

Parameters:
`label` - The label of the vertex sought.
Returns:
The actual label, or null if none is found.

### getEdge

```Edge<V,E> getEdge(V label1,
V label2)```
Get reference to actual edge. Edge is identified by the labels on associated vertices. If edge is directed, the label1 indicates source.

Parameters:
`label1` - The first (or source, if directed) vertex.
`label2` - The second (or destination, if directed) vertex.
Returns:
The edge, if found, or null.

### contains

`boolean contains(V label)`
Test for vertex membership.

Specified by:
`contains` in interface `Structure<V>`
Parameters:
`label` - The label of the vertex sought.
Returns:
True iff vertex with matching label is found.

### containsEdge

```boolean containsEdge(V vLabel1,
V vLabel2)```
Test for edge membership. If edges are directed, vLabel1 indicates source.

Parameters:
`vLabel1` - First (or source, if directed) vertex.
`vLabel2` - Second (or destination, if directed) vertex.
Returns:
True iff the edge exists within the graph.

### visit

`boolean visit(V label)`
Test and set visited flag of vertex

Parameters:
`label` - Label of vertex to be visited.
Returns:
Previous value of visited flag on vertex.

### visitEdge

`boolean visitEdge(Edge<V,E> e)`
Test and set visited flag of edge.

Parameters:
`e` - Edge object that is part of graph.
Returns:
Previous value of the Edge's visited flag.

### isVisited

`boolean isVisited(V label)`
Return visited flag of vertex.

Parameters:
`label` - Label of vertex.
Returns:
True if vertex has been visited.

### isVisitedEdge

`boolean isVisitedEdge(Edge<V,E> e)`
Return visited flag of edge.

Parameters:
`e` - Edge of graph to be considered.
Returns:
True if the edge has been visited.

### reset

`void reset()`
Clear visited flags of edges and vertices.

### size

`int size()`
Determine number of vertices within graph.

Specified by:
`size` in interface `Structure<V>`
Returns:
The number of vertices within graph.

### degree

`int degree(V label)`
Determine out degree of vertex.

Parameters:
`label` - Label associated with vertex.
Returns:
The number of edges with this vertex as source.

### edgeCount

`int edgeCount()`
Determine the number of edges in graph.

Returns:
Number of edges in graph.

### iterator

`Iterator<V> iterator()`
Construct vertex iterator. Vertices are not visited in any guaranteed order.

Specified by:
`iterator` in interface `Iterable<V>`
Specified by:
`iterator` in interface `Structure<V>`
Returns:
Iterator traversing vertices in graph.
`AbstractIterator`, `Iterator`, `Enumeration`, `Structure.elements()`

### neighbors

`Iterator<V> neighbors(V label)`
Construct an adjacent vertex iterator. Adjacent vertices (those on destination of edge, if directed) are considered, but not in any guaranteed order.

Parameters:
`label` - Label of the vertex.
Returns:
Iterator traversing the adjacent vertices of labeled vertex.

### edges

`Iterator<Edge<V,E>> edges()`
Construct an iterator over all edges. Every directed/undirected edge is considered exactly once. Order is not guaranteed.

Returns:
Iterator over edges.

### clear

`void clear()`
Remove all vertices (and thus, edges) of the graph.

Specified by:
`clear` in interface `Structure<V>`

### isEmpty

`boolean isEmpty()`
Determine if graph is empty.

Specified by:
`isEmpty` in interface `Structure<V>`
Returns:
True iff there are no vertices in graph.

### isDirected

`boolean isDirected()`
Determine if graph is directed.

Returns:
True iff the graph is directed.