Detailed Description

This class describes the common interface of all undirected graphs.

Like all concept classes, it only provides an interface without any sensible implementation. So any general algorithm for undirected graphs should compile with this class, but it will not run properly, of course. An actual graph implementation like ListGraph or SmartGraph may have additional functionality.

The undirected graphs also fulfill the concept of directed graphs, since each edge can also be regarded as two oppositely directed arcs. Undirected graphs provide an Edge type for the undirected edges and an Arc type for the directed arcs. The Arc type is convertible to Edge or inherited from it, i.e. the corresponding edge can be obtained from an arc. EdgeIt and EdgeMap classes can be used for the edges, while ArcIt and ArcMap classes can be used for the arcs (just like in digraphs). Both InArcIt and OutArcIt iterates on the same edges but with opposite direction. IncEdgeIt also iterates on the same edges as OutArcIt and InArcIt, but it is not convertible to Arc, only to Edge.

In LEMON, each undirected edge has an inherent orientation. Thus it can defined if an arc is forward or backward oriented in an undirected graph with respect to this default oriantation of the represented edge. With the direction() and direct() functions the direction of an arc can be obtained and set, respectively.

Only nodes and edges can be added to or removed from an undirected graph and the corresponding arcs are added or removed automatically.

See Also: Digraph

#include <lemon/concepts/graph.h>

Classes
class	Arc
	The arc type of the graph. More...

class	ArcIt
	Iterator class for the arcs. More...

class	ArcMap
	Standard graph map type for the arcs. More...

class	Edge
	The edge type of the graph. More...

class	EdgeIt
	Iterator class for the edges. More...

class	EdgeMap
	Standard graph map type for the edges. More...

class	InArcIt
	Iterator class for the incoming arcs of a node. More...

class	IncEdgeIt
	Iterator class for the incident edges of a node. More...

class	Node
	The node type of the graph. More...

class	NodeIt
	Iterator class for the nodes. More...

class	NodeMap
	Standard graph map type for the nodes. More...

class	OutArcIt
	Iterator class for the outgoing arcs of a node. More...

Public Types
typedef True	UndirectedTag
	Undirected graphs should be tagged with `UndirectedTag`. More...

Public Member Functions
	Graph ()
	Default constructor.

Node	u (Edge) const
	The first node of the edge. More...

Node	v (Edge) const
	The second node of the edge. More...

Node	source (Arc) const
	The source node of the arc. More...

Node	target (Arc) const
	The target node of the arc. More...

int	id (Node) const
	The ID of the node. More...

int	id (Edge) const
	The ID of the edge. More...

int	id (Arc) const
	The ID of the arc. More...

Node	nodeFromId (int) const
	The node with the given ID. More...

Edge	edgeFromId (int) const
	The edge with the given ID. More...

Arc	arcFromId (int) const
	The arc with the given ID. More...

int	maxNodeId () const
	An upper bound on the node IDs. More...

int	maxEdgeId () const
	An upper bound on the edge IDs. More...

int	maxArcId () const
	An upper bound on the arc IDs. More...

bool	direction (Arc) const
	The direction of the arc. More...

Arc	direct (Edge, bool) const
	Direct the edge. More...

Arc	direct (Edge, Node) const
	Direct the edge. More...

Arc	oppositeArc (Arc) const
	The oppositely directed arc. More...

Node	oppositeNode (Node, Edge) const
	The opposite node on the edge. More...

Node	baseNode (IncEdgeIt) const
	The base node of the iterator. More...

Node	runningNode (IncEdgeIt) const
	The running node of the iterator. More...

Node	baseNode (OutArcIt) const
	The base node of the iterator. More...

Node	runningNode (OutArcIt) const
	The running node of the iterator. More...

Node	baseNode (InArcIt) const
	The base node of the iterator. More...

Node	runningNode (InArcIt) const
	The running node of the iterator. More...

Private Member Functions
	Graph (const Graph &)
	Graphs are not copy constructible. Use GraphCopy instead.

void	operator= (const Graph &)
	Assignment of a graph to another one is not allowed. Use GraphCopy instead.

Member Typedef Documentation

typedef True UndirectedTag

Undirected graphs should be tagged with UndirectedTag.

This tag helps the enable_if technics to make compile time specializations for undirected graphs.

Member Function Documentation

Node u ( Edge ) const

inline

Returns the first node of the given edge.

Edges don't have source and target nodes, however, methods u() and v() are used to query the two end-nodes of an edge. The orientation of an edge that arises this way is called the inherent direction, it is used to define the default direction for the corresponding arcs.

See Also: v(); direction()

Node v ( Edge ) const

inline

Returns the second node of the given edge.

Edges don't have source and target nodes, however, methods u() and v() are used to query the two end-nodes of an edge. The orientation of an edge that arises this way is called the inherent direction, it is used to define the default direction for the corresponding arcs.

See Also: u(); direction()

Node source ( Arc ) const

inline

Returns the source node of the given arc.

Node target ( Arc ) const

inline

Returns the target node of the given arc.

int id ( Node ) const

inline

Returns the ID of the given node.

int id ( Edge ) const

inline

Returns the ID of the given edge.

int id ( Arc ) const

inline

Returns the ID of the given arc.

Node nodeFromId ( int ) const

inline

Returns the node with the given ID.

Precondition: The argument should be a valid node ID in the graph.

Edge edgeFromId ( int ) const

inline

Returns the edge with the given ID.

Precondition: The argument should be a valid edge ID in the graph.

Arc arcFromId ( int ) const

inline

Returns the arc with the given ID.

Precondition: The argument should be a valid arc ID in the graph.

int maxNodeId ( ) const

inline

Returns an upper bound on the node IDs.

int maxEdgeId ( ) const

inline

Returns an upper bound on the edge IDs.

int maxArcId ( ) const

inline

Returns an upper bound on the arc IDs.

bool direction ( Arc ) const

inline

Returns true if the direction of the given arc is the same as the inherent orientation of the represented edge.

Arc direct	(	Edge	,
		bool
	)		const

inline

Direct the given edge. The returned arc represents the given edge and its direction comes from the bool parameter. If it is true, then the direction of the arc is the same as the inherent orientation of the edge.

Arc direct	(	Edge	,
		Node
	)		const

inline

Direct the given edge. The returned arc represents the given edge and its source node is the given node.

Arc oppositeArc ( Arc ) const

inline

Returns the oppositely directed arc representing the same edge.

Node oppositeNode	(	Node	,
		Edge
	)		const

inline

Returns the opposite node on the given edge.

Node baseNode ( IncEdgeIt ) const

inline

Returns the base node of the given incident edge iterator.

Node runningNode ( IncEdgeIt ) const

inline

Returns the running node of the given incident edge iterator.

Node baseNode ( OutArcIt ) const

inline

Returns the base node of the given outgoing arc iterator (i.e. the source node of the corresponding arc).

Node runningNode ( OutArcIt ) const

inline

Returns the running node of the given outgoing arc iterator (i.e. the target node of the corresponding arc).

Node baseNode ( InArcIt ) const

inline

Returns the base node of the given incoming arc iterator (i.e. the target node of the corresponding arc).

Node runningNode ( InArcIt ) const

inline

Returns the running node of the given incoming arc iterator (i.e. the source node of the corresponding arc).

Detailed Description

Classes

Public Types

Public Member Functions

Private Member Functions

Member Typedef Documentation

Member Function Documentation