Ubuntu Manpage: struct::graph - Create and manipulate directed graph objects

NAME

       struct::graph - Create and manipulate directed graph objects

SYNOPSIS

       package require Tcl  8.4

       package require struct::graph  ?2.4.3?

       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 arcx.

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 -embedding 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.

Attention: After the above options any word with a leading dash which is not a
valid option is treated as a node name instead of an invalid option to error out
on. This condition holds until either a valid option terminates the list of nodes,
or the end of the command is reached, whichever comes first.

The remaining filter options are:

-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. Note that while the
exact meanings change slightly, as they operate on nodes instead of arcs, the
general behaviour is the same, especially when it comes to the handling of words
with a leading dash in node lists.

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.

       When proposing code changes, please provide unified diffs, i.e the output of diff -u.

       Note further that attachments are strongly preferred over inlined patches. Attachments can
       be made by going to the Edit form of the ticket immediately after its creation,  and  then
       using the left-most button in the secondary navigation bar.

KEYWORDS

       adjacent,  arc,  cgraph,  degree,  edge,  graph,  loop,  neighbour,  node,  serialization,
       subgraph, vertex

COPYRIGHT

       Copyright (c) 2002-2009,2019 Andreas Kupries <andreas_kupries@users.sourceforge.net>