NAME¶
struct::graph - Create and manipulate directed graph objects
SYNOPSIS¶
package require
Tcl 8.4
package require
struct::graph ?2.4?
package require
struct::list ?1.5?
package require
struct::set ?2.2.3?
::struct::graph ?
graphName?
?
=|
:=|
as|
deserialize source?
graphName option ?
arg arg ...?
graphName = sourcegraph
graphName --> destgraph
graphName append key value
graphName deserialize serialization
graphName destroy
graphName arc append arc key value
graphName arc attr key
graphName arc attr key -arcs list
graphName arc attr key -glob globpattern
graphName arc attr key -regexp repattern
graphName arc delete arc ?
arc ...?
graphName arc exists arc
graphName arc flip arc
graphName arc get arc key
graphName arc getall arc ?
pattern?
graphName arc getunweighted
graphName arc getweight arc
graphName arc keys arc ?
pattern?
graphName arc keyexists arc key
graphName arc insert start end ?
child?
graphName arc lappend arc key value
graphName arc rename arc newname
graphName arc set arc key ?
value?
graphName arc setunweighted ?
weight?
graphName arc setweight arc weight
graphName arc unsetweight arc
graphName arc hasweight arc
graphName arc source arc
graphName arc target arc
graphName arc nodes arc
graphName arc move-source arc newsource
graphName arc move-target arc newtarget
graphName arc move arc newsource newtarget
graphName arc unset arc key
graphName arc weights
graphName arcs ?-key
key? ?-value
value? ?-filter
cmdprefix? ?-in|-out|-adj|-inner|-embedding
node node...?
graphName lappend key value
graphName node append node key value
graphName node attr key
graphName node attr key -nodes list
graphName node attr key -glob globpattern
graphName node attr key -regexp repattern
graphName node degree ?-in|-out?
node
graphName node delete node ?
node...?
graphName node exists node
graphName node get node key
graphName node getall node ?
pattern?
graphName node keys node ?
pattern?
graphName node keyexists node key
graphName node insert ?
node...?
graphName node lappend node key value
graphName node opposite node arc
graphName node rename node newname
graphName node set node key ?
value?
graphName node unset node key
graphName nodes ?-key
key? ?-value
value? ?-filter
cmdprefix? ?-in|-out|-adj|-inner|-embedding
node node...?
graphName get key
graphName getall ?
pattern?
graphName keys ?
pattern?
graphName keyexists key
graphName serialize ?
node...?
graphName set key ?
value?
graphName swap node1 node2
graphName unset key
graphName walk node ?-order
order? ?-type
type? ?-dir
direction? -command
cmd
DESCRIPTION¶
A directed graph is a structure containing two collections of elements, called
nodes and
arcs respectively, together with a relation
("connectivity") that places a general structure upon the nodes and
arcs.
Each arc is connected to two nodes, one of which is called the
source and
the other the
target. This imposes a direction upon the arc, which is
said to go from the source to the target. It is allowed that source and target
of an arc are the same node. Such an arc is called a
loop. Whenever a
node is either the source or target of an arc both are said to be
adjacent. This extends into a relation between nodes, i.e. if two nodes
are connected through at least one arc they are said to be
adjacent
too.
Each node can be the source and target for any number of arcs. The former are
called the
outgoing arcs of the node, the latter the
incoming
arcs of the node. The number of arcs in either set is called the
in-degree resp. the
out-degree of the node.
In addition to maintaining the node and arc relationships, this graph
implementation allows any number of named
attributes to be associated
with the graph itself, and each node or arc.
Note: The major version of the package
struct has been changed to
version 2.0, due to backward incompatible changes in the API of this module.
Please read the section
Changes for 2.0 for a full list of all changes,
incompatible and otherwise.
Note: A C-implementation of the command can be had from the location
http://www.purl.org/NET/schlenker/tcl/cgraph. See also
http://wiki.tcl.tk/cgraph. This implementation uses a bit less memory
than the tcl version provided here directly, and is faster. Its support is
limited to versions of the package before 2.0.
As of version 2.2 of this package a critcl based C implementation is available
from here as well. This implementation however requires Tcl 8.4 to run.
The main command of the package is:
- ::struct::graph ?graphName?
?=|:=|as|deserialize source?
- The command creates a new graph object with an associated global Tcl
command whose name is graphName. This command may be used to invoke
various operations on the graph. It has the following general form:
- graphName option ?arg arg ...?
- Option and the args determine the exact behavior of the
command.
If
graphName is not specified a unique name will be generated by the
package itself. If a
source is specified the new graph will be
initialized to it. For the operators
=,
:=, and
as the
source argument is interpreted as the name of another graph object, and
the assignment operator
= will be executed. For the operator
deserialize the
source is a serialized graph object and
deserialize will be executed.
In other words
::struct::graph mygraph = b
is equivalent to
::struct::graph mygraph
mygraph = b
and
::struct::graph mygraph deserialize $b
is equivalent to
::struct::graph mygraph
mygraph deserialize $b
The following commands are possible for graph objects:
- graphName = sourcegraph
- This is the assignment operator for graph objects. It copies the
graph contained in the graph object sourcegraph over the graph data
in graphName. The old contents of graphName are deleted by
this operation.
This operation is in effect equivalent to
graphName deserialize [sourcegraph serialize]
The operation assumes that the
sourcegraph provides the method
serialize and that this method returns a valid graph serialization.
- graphName --> destgraph
- This is the reverse assignment operator for graph objects. It
copies the graph contained in the graph object graphName over the
graph data in the object destgraph. The old contents of
destgraph are deleted by this operation.
This operation is in effect equivalent to
destgraph deserialize [graphName serialize]
The operation assumes that the
destgraph provides the method
deserialize and that this method takes a graph serialization.
- graphName append key value
- Appends a value to one of the keyed values associated with the
graph. Returns the new value given to the attribute key.
- graphName deserialize serialization
- This is the complement to serialize. It replaces the graph data in
graphName with the graph described by the serialization
value. The old contents of graphName are deleted by this
operation.
- graphName destroy
- Destroys the graph, including its storage space and associated
command.
- graphName arc append arc key value
- Appends a value to one of the keyed values associated with an
arc. Returns the new value given to the attribute key.
- graphName arc attr key
- graphName arc attr key -arcs list
- graphName arc attr key -glob
globpattern
- graphName arc attr key -regexp
repattern
- This method retrieves the value of the attribute named key, for all
arcs in the graph (matching the restriction specified via one of the
possible options) and having the specified attribute.
The result is a dictionary mapping from arc names to the value of attribute
key at that arc. Arcs not having the attribute key, or not
passing a specified restriction, are not listed in the result.
The possible restrictions are:
- -arcs
- The value is a list of arcs. Only the arcs mentioned in this list are
searched for the attribute.
- -glob
- The value is a glob pattern. Only the arcs in the graph whose names match
this pattern are searched for the attribute.
- -regexp
- The value is a regular expression. Only the arcs in the graph whose names
match this pattern are searched for the attribute.
- graphName arc delete arc ?arc ...?
- Remove the specified arcs from the graph.
- graphName arc exists arc
- Return true if the specified arc exists in the graph.
- graphName arc flip arc
- Reverses the direction of the named arc, i.e. the source and target
nodes of the arc are exchanged with each other.
- graphName arc get arc key
- Returns the value associated with the key key for the
arc.
- graphName arc getall arc ?pattern?
- Returns a dictionary (suitable for use with [array set]) for the
arc. If the pattern is specified only the attributes whose
names match the pattern will be part of the returned dictionary. The
pattern is a glob pattern.
- graphName arc getunweighted
- Returns a list containing the names of all arcs in the graph which have no
weight associated with them.
- graphName arc getweight arc
- Returns the weight associated with the arc. Throws an error if the
arc has no weight associated with it.
- graphName arc keys arc ?pattern?
- Returns a list of keys for the arc. If the pattern is
specified only the attributes whose names match the pattern will be part
of the returned list. The pattern is a glob pattern.
- graphName arc keyexists arc key
- Return true if the specified key exists for the arc.
- graphName arc insert start end
?child?
- Insert an arc named child into the graph beginning at the node
start and ending at the node end. If the name of the new arc
is not specified the system will generate a unique name of the form
arc x.
- graphName arc lappend arc key
value
- Appends a value (as a list) to one of the keyed values associated
with an arc. Returns the new value given to the attribute
key.
- graphName arc rename arc newname
- Renames the arc arc to newname. An error is thrown if either
the arc does not exist, or a arc with name newname does exist. The
result of the command is the new name of the arc.
- graphName arc set arc key ?value?
- Set or get one of the keyed values associated with an arc. An arc may have
any number of keyed values associated with it. If value is not
specified, this command returns the current value assigned to the key; if
value is specified, this command assigns that value to the key, and
returns that value.
- graphName arc setunweighted ?weight?
- Sets the weight of all arcs without a weight to weight. Returns the
empty string as its result. If not present weight defaults to
0.
- graphName arc setweight arc weight
- Sets the weight of the arc to weight. Returns
weight.
- graphName arc unsetweight arc
- Removes the weight of the arc, if present. Does nothing otherwise.
Returns the empty string.
- graphName arc hasweight arc
- Determines if the arc has a weight associated with it. The result
is a boolean value, True if a weight is defined, and False
otherwise.
- graphName arc source arc
- Return the node the given arc begins at.
- graphName arc target arc
- Return the node the given arc ends at.
- graphName arc nodes arc
- Return the nodes the given arc begins and ends at, as a two-element
list.
- graphName arc move-source arc newsource
- Changes the source node of the arc to newsource. It can be said
that the arc rotates around its target node.
- graphName arc move-target arc newtarget
- Changes the target node of the arc to newtarget. It can be said
that the arc rotates around its source node.
- graphName arc move arc newsource
newtarget
- Changes both source and target nodes of the arc to newsource, and
newtarget resp.
- graphName arc unset arc key
- Remove a keyed value from the arc arc. The method will do nothing
if the key does not exist.
- graphName arc weights
- Returns a dictionary whose keys are the names of all arcs which have a
weight associated with them, and the values are these weights.
- graphName arcs ?-key key? ?-value value?
?-filter cmdprefix? ?-in|-out|-adj|-inner|-embedding node
node...?
- Returns a list of arcs in the graph. If no restriction is specified a list
containing all arcs is returned. Restrictions can limit the list of
returned arcs based on the nodes that are connected by the arc, on the
keyed values associated with the arc, or both. A general filter command
can be used as well. The restrictions that involve connected nodes take a
variable number of nodes as argument, specified after the name of the
restriction itself.
The restrictions imposed by either -in, -out, -adj,
-inner, or -embedded are applied first. Specifying more than
one of them is illegal.
After that the restrictions set via -key (and -value) are
applied. Specifying more than one -key (and -value) is
illegal. Specifying -value alone, without -key is illegal as
well.
Any restriction set through -filter is applied last. Specifying more
than one -filter is illegal.
Coming back to the restrictions based on a set of nodes, the command
recognizes the following switches:
- -in
- Return a list of all arcs whose target is one of the nodes in the set of
nodes. I.e. it computes the union of all incoming arcs of the nodes in the
set.
- -out
- Return a list of all arcs whose source is one of the nodes in the set of
nodes. I.e. it computes the union of all outgoing arcs of the nodes in the
set.
- -adj
- Return a list of all arcs adjacent to at least one of the nodes in the
set. This is the union of the nodes returned by -in and
-out.
- -inner
- Return a list of all arcs which are adjacent to two of the nodes in the
set. This is the set of arcs in the subgraph spawned by the specified
nodes.
- -embedding
- Return a list of all arcs adjacent to exactly one of the nodes in the set.
This is the set of arcs connecting the subgraph spawned by the specified
nodes to the rest of the graph.
- -key key
- Limit the list of arcs that are returned to those arcs that have an
associated key key.
- -value value
- This restriction can only be used in combination with -key. It
limits the list of arcs that are returned to those arcs whose associated
key key has the value value.
- -filter cmdrefix
- Limit the list of arcs that are returned to those arcs that pass the test.
The command in cmdprefix is called with two arguments, the name of
the graph object, and the name of the arc in question. It is executed in
the context of the caller and has to return a boolean value. Arcs for
which the command returns false are removed from the result list
before it is returned to the caller.
- graphName lappend key value
- Appends a value (as a list) to one of the keyed values associated
with the graph. Returns the new value given to the attribute
key.
- graphName node append node key
value
- Appends a value to one of the keyed values associated with an
node. Returns the new value given to the attribute key.
- graphName node attr key
- graphName node attr key -nodes
list
- graphName node attr key -glob
globpattern
- graphName node attr key -regexp
repattern
- This method retrieves the value of the attribute named key, for all
nodes in the graph (matching the restriction specified via one of the
possible options) and having the specified attribute.
The result is a dictionary mapping from node names to the value of attribute
key at that node. Nodes not having the attribute key, or not
passing a specified restriction, are not listed in the result.
The possible restrictions are:
- -nodes
- The value is a list of nodes. Only the nodes mentioned in this list are
searched for the attribute.
- -glob
- The value is a glob pattern. Only the nodes in the graph whose names match
this pattern are searched for the attribute.
- -regexp
- The value is a regular expression. Only the nodes in the graph whose names
match this pattern are searched for the attribute.
- graphName node degree ?-in|-out? node
- Return the number of arcs adjacent to the specified node. If one of
the restrictions -in or -out is given only the incoming
resp. outgoing arcs are counted.
- graphName node delete node ?node...?
- Remove the specified nodes from the graph. All of the nodes' arcs will be
removed as well to prevent unconnected arcs.
- graphName node exists node
- Return true if the specified node exists in the graph.
- graphName node get node key
- Return the value associated with the key key for the
node.
- graphName node getall node ?pattern?
- Returns a dictionary (suitable for use with [array set]) for the
node. If the pattern is specified only the attributes whose
names match the pattern will be part of the returned dictionary. The
pattern is a glob pattern.
- graphName node keys node ?pattern?
- Returns a list of keys for the node. If the pattern is
specified only the attributes whose names match the pattern will be part
of the returned list. The pattern is a glob pattern.
- graphName node keyexists node key
- Return true if the specified key exists for the node.
- graphName node insert ?node...?
- Insert one or more nodes into the graph. The new nodes have no arcs
connected to them. If no node is specified one node will be inserted, and
the system will generate a unique name of the form nodex for
it.
- graphName node lappend node key
value
- Appends a value (as a list) to one of the keyed values associated
with an node. Returns the new value given to the attribute
key.
- graphName node opposite node arc
- Return the node at the other end of the specified arc, which has to
be adjacent to the given node.
- graphName node rename node newname
- Renames the node node to newname. An error is thrown if
either the node does not exist, or a node with name newname does
exist. The result of the command is the new name of the node.
- graphName node set node key
?value?
- Set or get one of the keyed values associated with a node. A node may have
any number of keyed values associated with it. If value is not
specified, this command returns the current value assigned to the key; if
value is specified, this command assigns that value to the
key.
- graphName node unset node key
- Remove a keyed value from the node node. The method will do nothing
if the key does not exist.
- graphName nodes ?-key key? ?-value value?
?-filter cmdprefix? ?-in|-out|-adj|-inner|-embedding node
node...?
- Return a list of nodes in the graph. Restrictions can limit the list of
returned nodes based on neighboring nodes, or based on the keyed values
associated with the node. The restrictions that involve neighboring nodes
have a list of nodes as argument, specified after the name of the
restriction itself.
The possible restrictions are the same as for method arcs. The exact
meanings change slightly, as they operate on nodes instead of arcs. The
command recognizes:
- -in
- Return a list of all nodes with at least one outgoing arc ending in a node
found in the specified set of nodes. Alternatively specified as the set of
source nodes for the -in arcs of the node set. The incoming
neighbours.
- -out
- Return a list of all nodes with at least one incoming arc starting in a
node found in the specified set of nodes. Alternatively specified as the
set of target nodes for the -out arcs of the node set. The
outgoing neighbours.
- -adj
- This is the union of the nodes returned by -in and -out. The
neighbours.
- -inner
- The set of neighbours (see -adj above) which are also in the set of
nodes. I.e. the intersection between the set of nodes and the neighbours
per -adj.
- -embedding
- The set of neighbours (see -adj above) which are not in the set of
nodes. I.e. the difference between the neighbours as per -adj, and
the set of nodes.
- -key key
- Limit the list of nodes that are returned to those nodes that have an
associated key key.
- -value value
- This restriction can only be used in combination with -key. It
limits the list of nodes that are returned to those nodes whose associated
key key has the value value.
- -filter cmdrefix
- Limit the list of nodes that are returned to those nodes that pass the
test. The command in cmdprefix is called with two arguments, the
name of the graph object, and the name of the node in question. It is
executed in the context of the caller and has to return a boolean value.
Nodes for which the command returns false are removed from the
result list before it is returned to the caller.
- graphName get key
- Return the value associated with the key key for the graph.
- graphName getall ?pattern?
- Returns a dictionary (suitable for use with [array set]) for the
whole graph. If the pattern is specified only the attributes whose
names match the pattern will be part of the returned dictionary. The
pattern is a glob pattern.
- graphName keys ?pattern?
- Returns a list of keys for the whole graph. If the pattern is
specified only the attributes whose names match the pattern will be part
of the returned list. The pattern is a glob pattern.
- graphName keyexists key
- Return true if the specified key exists for the whole graph.
- graphName serialize ?node...?
- This method serializes the sub-graph spanned up by the nodes. In
other words it returns a tcl value completely describing that graph. If no
nodes are specified the whole graph will be serialized. This allows, for
example, the transfer of graph objects (or parts thereof) over arbitrary
channels, persistence, etc. This method is also the basis for both the
copy constructor and the assignment operator.
The result of this method has to be semantically identical over all
implementations of the graph interface. This is what will enable us to
copy graph data between different implementations of the same interface.
The result is a list containing a multiple of three items, plus one! In
other words, '[llength $serial] % 3 == 1'. Valid values include 1, 4, 7,
...
The last element of the list is a dictionary containing the attributes
associated with the whole graph. Regarding the other elements; each triple
consists of
- [1]
- The name of the node to be described,
- [2]
- A dictionary containing the attributes associated with the node,
- [3]
- And a list describing all the arcs starting at that node.
The elements of the arc list are lists containing three or four elements each,
i.e.
- [1]
- The name of the arc described by the element,
- [2]
- A reference to the destination node of the arc. This reference is an
integer number given the index of that node in the main serialization
list. As that it is greater than or equal to zero, less than the length of
the serialization, and a multiple of three. Note: For internal
consistency no arc name may be used twice, whether in the same node, or at
some other node. This is a global consistency requirement for the
serialization.
- [3]
- And a dictionary containing the attributes associated with the arc.
- [4]
- The weight associated with the arc. This value is optional. Its
non-presence means that the arc in question has no weight associated with
it.
Note: This information is new, compared to the serialization of
graph 2.3 and earlier. By making it an optional element the new
format is maximally compatible with the old. This means that any graph not
using weights will generate a serialization which is still understood by
the older graph package. A serialization will not be understood any longer
by the older packages if, and only if the graph it was generated from
actually has arcs with weights.
For all attribute dictionaries they keys are the names of the attributes, and
the values are the values for each name.
Note: The order of the nodes in the serialization has no relevance, nor
has the order of the arcs per node.
# A possible serialization for the graph structure
#
# d -----> %2
# / ^ \\
# / / \\
# / b \\
# / / \\
# %1 <- a - %0 e
# ^ \\ /
# \\ c /
# \\ \\ /
# \\ v v
# f ------ %3
# is
#
# %3 {} {{f 6 {}}} %0 {} {{a 6 {}} {b 9 {}} {c 0 {}}} %1 {} {{d 9 {}}} %2 {} {{e 0 {}}} {}
#
# This assumes that the graph has neither attribute data nor weighted arcs.
- graphName set key ?value?
- Set or get one of the keyed values associated with a graph. A graph may
have any number of keyed values associated with it. If value is not
specified, this command returns the current value assigned to the key; if
value is specified, this command assigns that value to the
key.
- graphName swap node1 node2
- Swap the position of node1 and node2 in the graph.
- graphName unset key
- Remove a keyed value from the graph. The method will do nothing if the
key does not exist.
- graphName walk node ?-order order? ?-type
type? ?-dir direction? -command cmd
- Perform a breadth-first or depth-first walk of the graph starting at the
node node going in either the direction of outgoing or opposite to
the incoming arcs.
The type of walk, breadth-first or depth-first, is determined by the value
of type; bfs indicates breadth-first, dfs indicates
depth-first. Depth-first is the default.
The order of the walk, pre-order, post-order or both-order is determined by
the value of order; pre indicates pre-order, post
indicates post-order, both indicates both-order. Pre-order is the
default. Pre-order walking means that a node is visited before any of its
neighbors (as defined by the direction, see below). Post-order
walking means that a parent is visited after any of its neighbors.
Both-order walking means that a node is visited before and after
any of its neighbors. The combination of a breadth-first walk with post-
or both-order is illegal.
The direction of the walk is determined by the value of dir;
backward indicates the direction opposite to the incoming arcs,
forward indicates the direction of the outgoing arcs.
As the walk progresses, the command cmd will be evaluated at each
node, with the mode of the call ( enter or leave) and values
graphName and the name of the current node appended. For a
pre-order walk, all nodes are entered, for a post-order all nodes
are left. In a both-order walk the first visit of a node enters it,
the second visit leaves it.
CHANGES FOR 2.0¶
The following noteworthy changes have occurred:
- [1]
- The API for accessing attributes and their values has been simplified.
All functionality regarding the default attribute "data" has been
removed. This default attribute does not exist anymore. All accesses to
attributes have to specify the name of the attribute in question. This
backward incompatible change allowed us to simplify the signature
of all methods handling attributes.
Especially the flag -key is not required anymore, even more, its use
is now forbidden. Please read the documentation for the arc and node
methods set, get, getall, unset,
append, lappend, keyexists and keys for a
description of the new API's.
- [2]
- The methods keys and getall now take an optional pattern
argument and will return only attribute data for keys matching this
pattern.
- [3]
- Arcs and nodes can now be renamed. See the documentation for the methods
arc rename and node rename.
- [4]
- The structure has been extended with API's for the serialization and
deserialization of graph objects, and a number of operations based on them
(graph assignment, copy construction).
Please read the documentation for the methods serialize,
deserialize, =, and -->, and the documentation on
the construction of graph objects.
Beyond the copying of whole graph objects these new API's also enable the
transfer of graph objects over arbitrary channels and for easy
persistence.
- [5]
- A new method, attr, was added to both arc and node
allowing the query and retrieval of attribute data without regard to arc
and node relationships.
- [6]
- Both methods arcs and nodes have been extended with the
ability to select arcs and nodes based on an arbitrary filtering
criterium.
BUGS, IDEAS, FEEDBACK¶
This document, and the package it describes, will undoubtedly contain bugs and
other problems. Please report such in the category
struct :: graph of
the
Tcllib Trackers [
http://core.tcl.tk/tcllib/reportlist]. Please also
report any ideas for enhancements you may have for either package and/or
documentation.
KEYWORDS¶
adjacent, arc, cgraph, degree, edge, graph, loop, neighbour, node,
serialization, subgraph, vertex
CATEGORY¶
Data structures
COPYRIGHT¶
Copyright (c) 2002-2009 Andreas Kupries <andreas_kupries@users.sourceforge.net>