Undirected graph class. More...

#include <undirected_graph.hpp>

Inheritance diagram for lal::graphs::undirected_graph:

Public Member Functions
	undirected_graph () noexcept
	Empty constructor.

	undirected_graph (const uint64_t n) noexcept
	Constructor with number of nodes.

	undirected_graph (const undirected_graph &g) noexcept
	Copy constructor.

	undirected_graph (undirected_graph &&g) noexcept
	Move constructor.

virtual	~undirected_graph () noexcept
	Destructor.

undirected_graph &	operator= (const undirected_graph &g) noexcept
	Copy assignment operator.

undirected_graph &	operator= (undirected_graph &&g) noexcept
	Move assignment operator.

void	reserve_degree (const node u, const uint64_t d) noexcept
	Predicts that the degree of node u is d.

virtual undirected_graph &	add_node () noexcept
	Adds a vertex to the graph.

virtual undirected_graph &	remove_node (const node u, const bool norm=true, const bool check_norm=true) noexcept
	Remove a node from this graph.

virtual undirected_graph &	add_edge (const node s, const node t, const bool norm=true, const bool check_norm=true) noexcept
	Adds an edge to the graph.

undirected_graph &	add_edge_bulk (const node s, const node t) noexcept
	Adds an edge to the graph.

void	finish_bulk_add (const bool norm=true, const bool check=true) noexcept
	Completes the inner structure of the graph after adding a bulk of edges.

virtual undirected_graph &	add_edges (const std::vector< edge > &edges, const bool norm=true, const bool check_norm=true) noexcept
	Adds a list of edges to the graph.

virtual undirected_graph &	set_edges (const std::vector< edge > &edges, const bool norm=true, const bool check_norm=true) noexcept
	Sets the edges to the graph.

virtual undirected_graph &	remove_edge (const node s, const node t, const bool norm=true, const bool check_norm=true) noexcept
	Remove an edge from this graph.

virtual undirected_graph &	remove_edge_bulk (const node s, const node t) noexcept
	Removes an edge from the graph.

void	finish_bulk_remove (const bool norm=true, const bool check=true) noexcept
	Completes the inner structure of the graph after removing edges in bulk.

virtual undirected_graph &	remove_edges (const std::vector< edge > &edges, const bool norm=true, const bool check_norm=true) noexcept
	Remove an edge from this graph.

virtual undirected_graph &	remove_edges_incident_to (const node u, const bool norm=true, const bool check_norm=true) noexcept
	Remove all edges incident to a given vertex.

undirected_graph &	disjoint_union (const undirected_graph &g) noexcept
	Disjoint union of graphs.

std::vector< edge_pair >	get_Q () const noexcept
	Returns all independent pairs of edges of this graph.

std::vector< edge >	get_edges () const noexcept
	Returns all edges of this graph.

const neighbourhood &	get_neighbors (const node u) const noexcept
	Returns the neighbourhood of node u.

uint64_t	get_degree (const node u) const noexcept
	Returns the number of neighbors of u.

bool	has_edge (const node u, const node v) const noexcept
	Returns true if the edge \(\{u,v\}\) exists in the graph.

bool	is_directed () const noexcept
	Returns whether this graph is directed or not.

bool	is_undirected () const noexcept
	Returns whether this graph is undirected or not.

std::vector< undirected_graph >	get_connected_components () const noexcept
	Returns all the connected components of this graph as individual graphs.

virtual void	init (const uint64_t n) noexcept
	Allocates the necessary memory for this class.

virtual void	clear () noexcept
	Frees the memory occupied by this graph.

virtual void	normalize () noexcept
	Normalizes the graph.

virtual bool	check_normalized () noexcept
	Checks if the graph is normalized.

void	set_normalized (const bool v=true) noexcept
	Sets whether this graph is normalized or not.

bool	has_node (const node u) const noexcept
	Returns true if node u is in this graph.

uint64_t	get_num_nodes () const noexcept
	Returns the number of ndoes.

uint64_t	get_num_edges () const noexcept
	Returns the number of edges.

bool	is_normalized () const noexcept
	Returns whether this graph is normalized or not.

Protected Member Functions
virtual void	_init (const uint64_t n) noexcept
	Initializes the memory in the graph hierarchy.

virtual void	_clear () noexcept
	Clears the memory of undirected_graph and graph classes.

virtual void	actions_after_add_edge (const node u, const node v) noexcept
	Do some extra work after the addition of an edge.

virtual void	actions_after_add_edges (const edge_list &e) noexcept
	Do some extra work after the addition of several edges.

virtual void	actions_after_add_edges_bulk () noexcept
	Do some extra work after the addition of several edges in bulk.

virtual void	actions_after_remove_edge (const node u, const node v) noexcept
	Do some extra work after the removal of an edge.

virtual void	actions_after_remove_edges (const edge_list &e) noexcept
	Do some extra work after the removal of several edges.

virtual void	actions_after_remove_edges_bulk () noexcept
	Do some extra work after the removal of several edges in bulk.

virtual void	actions_before_remove_edges_incident_to (const node u) noexcept
	Do some work before all edges incident to a node is removed.

virtual void	actions_after_remove_node (const node u) noexcept
	Do some work before the removal of a vertex.

void	copy_full_undirected_graph (const undirected_graph &u) noexcept
	Copies all members of this class and the parent class.

void	move_full_undirected_graph (undirected_graph &&u) noexcept
	Moves all members of this class and the parent class.

void	copy_full_graph (const graph &g) noexcept
	Copies all members of this class.

void	move_full_graph (graph &&g) noexcept
	Moves all members of this class.

void	__add_node () noexcept
	Adds a node to the graph.

void	__disjoint_union (const graph &g) noexcept
	Disjoint union of graphs.

void	normalize_after_edge_addition (const bool norm, const bool check) noexcept
	Normalize the graph after one (or more) edges have been added.

void	normalize_after_edge_removal (const bool norm, const bool check) noexcept
	Normalize the graph after one (or more) edges have been removed.

Protected Attributes
std::vector< neighbourhood >	m_adjacency_list
	Data structure that implements the graph.

uint64_t	m_num_edges = 0
	Amount of edges of this graph.

bool	m_is_normalized = true
	Is this graph normalized?

Private Member Functions
void	remove_single_edge (const node u, const node v, neighbourhood &out_u, neighbourhood &in_v) noexcept
	Removes a single edge.

Detailed Description

Undirected graph class.

Class implementing an undirected graph, using the adjacency list data structure.

An object of this class must be initialized either with its constructor or with the init method. Edges can then be added one by one (see add_edge) or all at the same time (see add_edges).

Constructor & Destructor Documentation

◆ undirected_graph() [1/3]

lal::graphs::undirected_graph::undirected_graph ( const uint64_t n )

inlinenoexcept

Constructor with number of nodes.

Parameters

n	Number of nodes.

◆ undirected_graph() [2/3]

lal::graphs::undirected_graph::undirected_graph ( const undirected_graph & g )

inlinenoexcept

Copy constructor.

Parameters

g	Undirected graph.

◆ undirected_graph() [3/3]

lal::graphs::undirected_graph::undirected_graph ( undirected_graph && g )

inlinenoexcept

Move constructor.

Parameters

g	Undirected graph.

Member Function Documentation

◆ __disjoint_union()

void lal::graphs::graph::__disjoint_union ( const graph & g )

protectednoexceptinherited

Disjoint union of graphs.

Given a graph, append it to the current graph.

All the nodes in g are relabelled starting at n, the number of nodes of the current graph.

Parameters

g	Input graph.

Precondition: This graph and g must be of the same type (both must be either undirected, or both directed).

Postcondition: The graph is normalized only if it was normalized before the call and g is also normalized.

◆ _init()

virtual void lal::graphs::undirected_graph::_init ( const uint64_t n )

inlineprotectedvirtualnoexcept

Initializes the memory in the graph hierarchy.

Initializes memory of lal::graphs::undirected_graph and lal::graphs::graph classes.

Parameters

n	Number of nodes

Precondition: The graph is cleared.

Reimplemented from lal::graphs::graph.

Reimplemented in lal::graphs::free_tree.

◆ actions_after_add_edge()

virtual void lal::graphs::undirected_graph::actions_after_add_edge	(	const node	u,
		const node	v )

protectedvirtualnoexcept

Do some extra work after the addition of an edge.

Parameters

u	Node of the edge
v	Node of the edge

Reimplemented from lal::graphs::graph.

Reimplemented in lal::graphs::free_tree.

◆ actions_after_add_edges()

virtual void lal::graphs::undirected_graph::actions_after_add_edges ( const edge_list & e )

protectedvirtualnoexcept

Do some extra work after the addition of several edges.

Parameters

e	List of edges.

Reimplemented from lal::graphs::graph.

Reimplemented in lal::graphs::free_tree.

◆ actions_after_add_edges_bulk()

virtual void lal::graphs::undirected_graph::actions_after_add_edges_bulk ( )

protectedvirtualnoexcept

Do some extra work after the addition of several edges in bulk.

This method should only be called after several calls to undirected_graph::add_edge_bulk or directed_graph::add_edge_bulk.

Reimplemented from lal::graphs::graph.

Reimplemented in lal::graphs::free_tree.

◆ actions_after_remove_edge()

virtual void lal::graphs::undirected_graph::actions_after_remove_edge	(	const node	u,
		const node	v )

protectedvirtualnoexcept

Do some extra work after the removal of an edge.

Parameters

u	Node of the edge
v	Node of the edge

Reimplemented from lal::graphs::graph.

Reimplemented in lal::graphs::free_tree.

◆ actions_after_remove_edges()

virtual void lal::graphs::undirected_graph::actions_after_remove_edges ( const edge_list & e )

protectedvirtualnoexcept

Do some extra work after the removal of several edges.

Parameters

e	List of edges.

Reimplemented from lal::graphs::graph.

Reimplemented in lal::graphs::free_tree.

◆ actions_after_remove_edges_bulk()

virtual void lal::graphs::undirected_graph::actions_after_remove_edges_bulk ( )

protectedvirtualnoexcept

Do some extra work after the removal of several edges in bulk.

This method should only be called after several calls to undirected_graph::remove_edge_bulk or directed_graph::remove_edge_bulk.

Reimplemented from lal::graphs::graph.

Reimplemented in lal::graphs::free_tree.

◆ actions_after_remove_node()

virtual void lal::graphs::undirected_graph::actions_after_remove_node ( const node u )

protectedvirtualnoexcept

Do some work before the removal of a vertex.

Parameters

u	Node to be removed.

Reimplemented from lal::graphs::graph.

Reimplemented in lal::graphs::free_tree.

◆ actions_before_remove_edges_incident_to()

virtual void lal::graphs::undirected_graph::actions_before_remove_edges_incident_to ( const node u )

protectedvirtualnoexcept

Do some work before all edges incident to a node is removed.

Parameters

u	Node whose incident edges are to be removed.

Reimplemented from lal::graphs::graph.

Reimplemented in lal::graphs::free_tree.

◆ add_edge()

virtual undirected_graph & lal::graphs::undirected_graph::add_edge	(	const node	s,
		const node	t,
		const bool	norm = true,
		const bool	check_norm = true )

virtualnoexcept

Adds an edge to the graph.

Method actions_after_add_edge is called after the edge has been added.

Parameters

s	Valid node index: \(0 \le s < n\).
t	Valid node index: \(0 \le t < n\).
norm	Should the graph be normalized?
check_norm	If norm is false then, should we check whether the result is normalized or not? This might be useful in case the resulting graph is normalized. If norm is true then check_norm is ignored.

Precondition: \(u \neq v\).; The edge \(\{s,t\}\) is not part of the graph.

Postcondition: If norm is true the graph is guaranteed to be normalized after the addition of the edge.

Reimplemented in lal::graphs::free_tree.

◆ add_edge_bulk()

undirected_graph & lal::graphs::undirected_graph::add_edge_bulk	(	const node	s,
		const node	t )

noexcept

Adds an edge to the graph.

This method only adds an edge, and does no other work: normalisation is not checked, and no extra work per edge is done.

Parameters

s	Valid node index: \(0 \le s < n\).
t	Valid node index: \(0 \le t < n\).

Precondition: \(u \neq v\).; The edge \(\{s,t\}\) is not part of the graph.

Postcondition: If norm is true the graph is guaranteed to be normalized after the addition of the edge.

◆ add_edges()

virtual undirected_graph & lal::graphs::undirected_graph::add_edges	(	const std::vector< edge > &	edges,
		const bool	norm = true,
		const bool	check_norm = true )

virtualnoexcept

Adds a list of edges to the graph.

This operation is faster than calling add_edge since the edges are added in bulk.

Parameters

edges	The edges to be added.
norm	Normalize the graph after the insertions.
check_norm	If norm is false then, should we check whether the result is normalized or not? This might be useful in case the resulting graph is normalized. If norm is true then check_norm is ignored.

Precondition: All the edges in edges must meet the precondition of method add_edge(node,node,bool,bool).

Postcondition: If norm is true the graph is guaranteed to be normalized after the addition of the edges.

Reimplemented in lal::graphs::free_tree.

◆ check_normalized()

virtual bool lal::graphs::graph::check_normalized ( )

virtualnoexceptinherited

Checks if the graph is normalized.

Checks, whether the graph's adjacency structure is normalized or not. In case it is, attribute m_is_normalized is set to true, so method is_normalized evaluates to true.

Reimplemented in lal::graphs::directed_graph.

◆ clear()

virtual void lal::graphs::graph::clear ( )

virtualnoexceptinherited

Frees the memory occupied by this graph.

See _clear for details.

Postcondition: The graph is normalized. The number of edges is 0.

◆ disjoint_union()

undirected_graph & lal::graphs::undirected_graph::disjoint_union ( const undirected_graph & g )

noexcept

Disjoint union of graphs.

Given a graph, append it to the current graph.

All the nodes in g are relabelled starting at n, the number of nodes of the current graph.

Parameters

g	Input graph.

Postcondition: The graph is normalized only if it was normalized before the call and g is also normalized.

◆ finish_bulk_add()

void lal::graphs::undirected_graph::finish_bulk_add	(	const bool	norm = true,
		const bool	check = true )

virtualnoexcept

Completes the inner structure of the graph after adding a bulk of edges.

This is meant to be used after several calls to undirected_graph::add_edge_bulk, directed_graph::add_edge_bulk.

Parameters

norm	Normalize the graph.
check	Check wether the graph is normalized or not.

Implements lal::graphs::graph.

◆ finish_bulk_remove()

void lal::graphs::undirected_graph::finish_bulk_remove	(	const bool	norm = true,
		const bool	check = true )

virtualnoexcept

Completes the inner structure of the graph after removing edges in bulk.

This is meant to be used after several calls to undirected_graph::remove_edge_bulk, directed_graph::remove_edge_bulk.

Parameters

norm	Normalize the graph.
check	Check wether the graph is normalized or not.

Implements lal::graphs::graph.

◆ get_degree()

uint64_t lal::graphs::undirected_graph::get_degree ( const node u ) const

inlinenodiscardnoexcept

Returns the number of neighbors of u.

Parameters

u	Node to be queried.

Returns: The number of adjacent nodes.

◆ get_neighbors()

const neighbourhood & lal::graphs::undirected_graph::get_neighbors ( const node u ) const

inlinenodiscardnoexcept

Returns the neighbourhood of node u.

Parameters

u Node.

Returns: The list of nodes adjacent to node u.

◆ get_Q()

std::vector< edge_pair > lal::graphs::undirected_graph::get_Q ( ) const

nodiscardvirtualnoexcept

Returns all independent pairs of edges of this graph.

The set \(Q(G)\) is defined as the pairs of edges of \(G\), \(E(G) \times E(G)\), that are independent, that is, that share no nodes.

Implements lal::graphs::graph.

◆ init()

virtual void lal::graphs::graph::init ( const uint64_t n )

virtualnoexceptinherited

Allocates the necessary memory for this class.

See _init for details.

Parameters

n	Number of nodes.

◆ is_normalized()

bool lal::graphs::graph::is_normalized ( ) const

inlinenodiscardnoexceptinherited

Returns whether this graph is normalized or not.

A graph is normalized if every node's adjacency list is sorted increasingly. For this, use method normalize().

Returns: The value of m_is_normalized.

◆ normalize()

virtual void lal::graphs::graph::normalize ( )

virtualnoexceptinherited

Normalizes the graph.

Sorts this graph's adjacency list structure in increasing order.

Besides expensive, this method may be unnecessary. Method check_normalized() checks whether the graph is normalized or not; in case it is, using this method is completely unnecessary.

Postcondition: Method is_normalized evaluates to true.

Reimplemented in lal::graphs::directed_graph.

◆ operator=() [1/2]

undirected_graph & lal::graphs::undirected_graph::operator= ( const undirected_graph & g )

inlinenoexcept

Copy assignment operator.

Parameters

g	Undirected graph.

◆ operator=() [2/2]

undirected_graph & lal::graphs::undirected_graph::operator= ( undirected_graph && g )

inlinenoexcept

Move assignment operator.

Parameters

g	Undirected graph.

◆ remove_edge()

virtual undirected_graph & lal::graphs::undirected_graph::remove_edge	(	const node	s,
		const node	t,
		const bool	norm = true,
		const bool	check_norm = true )

virtualnoexcept

Remove an edge from this graph.

Method actions_after_remove_edge is called after the edge has been removed.

Parameters

s	Valid node index: \(0 \le s < n\).
t	Valid node index: \(0 \le t < n\).
norm	Normalize the graph after the deletion.
check_norm	If norm is false then, should we check whether the result is normalized or not? This might be useful in case the resulting graph is normalized. If norm is true then check_norm is ignored.

Precondition: The edge must exist.

Postcondition: If norm is true the graph is guaranteed to be normalized after the addition of the edge.

Reimplemented in lal::graphs::free_tree.

◆ remove_edge_bulk()

virtual undirected_graph & lal::graphs::undirected_graph::remove_edge_bulk	(	const node	s,
		const node	t )

virtualnoexcept

Removes an edge from the graph.

This method only removes an edge, and does no other work: normalisation is not checked, and no extra work per edge is done.

Parameters

s	Valid node index: \(0 \le s < n\).
t	Valid node index: \(0 \le t < n\).

Precondition: \(u \neq v\).; The edge \(\{s,t\}\) is part of the graph.

Postcondition: If norm is true the graph is guaranteed to be normalized after the removal of the edge.

Reimplemented in lal::graphs::free_tree.

◆ remove_edges()

virtual undirected_graph & lal::graphs::undirected_graph::remove_edges	(	const std::vector< edge > &	edges,
		const bool	norm = true,
		const bool	check_norm = true )

virtualnoexcept

Remove an edge from this graph.

This operation is faster than removing edges one by one with remove_edge since the edges are removed in bulk.

Parameters

edges	The edges to be added.
norm	Normalize the graph after the deletion.
check_norm	If norm is false then, should we check whether the result is normalized or not? This might be useful in case the resulting graph is normalized. If norm is true then check_norm is ignored.

Precondition: All the edges in edges must meet the precondition of method add_edge(node,node,bool,bool).

Postcondition: If norm is true the graph is guaranteed to be normalized after the addition of the edge.

Reimplemented in lal::graphs::free_tree.

◆ remove_edges_incident_to()

virtual undirected_graph & lal::graphs::undirected_graph::remove_edges_incident_to	(	const node	u,
		const bool	norm = true,
		const bool	check_norm = true )

virtualnoexcept

Remove all edges incident to a given vertex.

This operation is faster than removing edges one by one with remove_edge since the edges are removed in bulk.

Method actions_after_remove_edge is called after each edge has been removed.

Parameters

u	The node whose incident vertices are to be removed.
norm	Normalize the graph after the deletion.
check_norm	If norm is false then, should we check whether the result is normalized or not? This might be useful in case the resulting graph is normalized. If norm is true then check_norm is ignored.

Postcondition: If norm is true the graph is guaranteed to be normalized after the addition of the edge.

Reimplemented in lal::graphs::free_tree.

◆ remove_node()

virtual undirected_graph & lal::graphs::undirected_graph::remove_node	(	const node	u,
		const bool	norm = true,
		const bool	check_norm = true )

virtualnoexcept

Remove a node from this graph.

Parameters

u	Valid node index: \(0 \le u < n\).
norm	Normalize the graph after the deletion.
check_norm	If norm is false then, should we check whether the result is normalized or not? This might be useful in case the resulting graph is normalized. If norm is true then check_norm is ignored.

Precondition: The node must exist.

Postcondition: If norm is true the graph is guaranteed to be normalized after the addition of the edge.

Reimplemented in lal::graphs::free_tree.

◆ remove_single_edge()

void lal::graphs::undirected_graph::remove_single_edge	(	const node	u,
		const node	v,
		neighbourhood &	out_u,
		neighbourhood &	in_v )

privatenoexcept

Removes a single edge.

Parameters

u	First node of edge.
v	Second node of edge.
out_u	Out-neighbourhood of node u.
in_v	In-neighbourhood of node v.

◆ reserve_degree()

void lal::graphs::undirected_graph::reserve_degree	(	const node	u,
		const uint64_t	d )

inlinenoexcept

Predicts that the degree of node u is d.

Memory of size d is reserved so that adding edges is done more efficiently.

Parameters

u	Node to reserve the degree for.
d	The amount of memory to reserve.

Precondition: The graph must have been initialized.

◆ set_edges()

virtual undirected_graph & lal::graphs::undirected_graph::set_edges	(	const std::vector< edge > &	edges,
		const bool	norm = true,
		const bool	check_norm = true )

virtualnoexcept

Sets the edges to the graph.

This list of edges is assumed to be all the edges that are going to be added to this graph. This means that the internal data structures are constructed more efficiently than when adding edges one by one (see add_edge) or in several chunks (see add_edges).

The current structure of the graph is cleared before setting the new edges.

Parameters

edges	The edges to be added.
norm	Normalize the graph after the insertions.
check_norm	If norm is false then, should we check whether the result is normalized or not? This might be useful in case the resulting graph is normalized. If norm is true then check_norm is ignored.

Precondition: The graph has been initialized with as many nodes as vertices in the list of edges.; All the edges in edges must meet the precondition of method add_edge(node,node,bool,bool).

Postcondition: If norm is true the graph is guaranteed to be normalized after the addition of the edge.

Reimplemented in lal::graphs::free_tree.

Member Data Documentation

◆ m_is_normalized

bool lal::graphs::graph::m_is_normalized = true

protectedinherited

Is this graph normalized?

An undirected graph is normalized iff every node's adjacency list is sorted in increasing order.

In directed graphs, however, it is necessary that the adjacency lists of the out-neighbors and in-neighbors of nodes be sorted.

This attribute is set to 'true' in all graph's initialisation and destruction (when clear() method is called).

The documentation for this class was generated from the following file:

lal/graphs/undirected_graph.hpp

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ undirected_graph() [1/3]

◆ undirected_graph() [2/3]

◆ undirected_graph() [3/3]

Member Function Documentation

◆ __disjoint_union()

◆ _init()

◆ actions_after_add_edge()

◆ actions_after_add_edges()

◆ actions_after_add_edges_bulk()

◆ actions_after_remove_edge()

◆ actions_after_remove_edges()

◆ actions_after_remove_edges_bulk()

◆ actions_after_remove_node()

◆ actions_before_remove_edges_incident_to()

◆ add_edge()

◆ add_edge_bulk()

◆ add_edges()

◆ check_normalized()

◆ clear()

◆ disjoint_union()

◆ finish_bulk_add()

◆ finish_bulk_remove()

◆ get_degree()

◆ get_neighbors()

◆ get_Q()

◆ init()

◆ is_normalized()

◆ normalize()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ remove_edge()

◆ remove_edge_bulk()

◆ remove_edges()

◆ remove_edges_incident_to()

◆ remove_node()

◆ remove_single_edge()

◆ reserve_degree()

◆ set_edges()

Member Data Documentation

◆ m_is_normalized