graph(3tcl)
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
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
-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>
Opportunity
Personal Opportunity - Free software gives you access to billions of dollars of software at no cost. Use this software for your business, personal use or to develop a profitable skill. Access to source code provides access to a level of capabilities/information that companies protect though copyrights. Open source is a core component of the Internet and it is available to you. Leverage the billions of dollars in resources and capabilities to build a career, establish a business or change the world. The potential is endless for those who understand the opportunity.
Business Opportunity - Goldman Sachs, IBM and countless large corporations are leveraging open source to reduce costs, develop products and increase their bottom lines. Learn what these companies know about open source and how open source can give you the advantage.
Free Software
Free Software provides computer programs and capabilities at no cost but more importantly, it provides the freedom to run, edit, contribute to, and share the software. The importance of free software is a matter of access, not price. Software at no cost is a benefit but ownership rights to the software and source code is far more significant.
Free Office Software - The Libre Office suite provides top desktop productivity tools for free. This includes, a word processor, spreadsheet, presentation engine, drawing and flowcharting, database and math applications. Libre Office is available for Linux or Windows.
Free Books
The Free Books Library is a collection of thousands of the most popular public domain books in an online readable format. The collection includes great classical literature and more recent works where the U.S. copyright has expired. These books are yours to read and use without restrictions.
Source Code - Want to change a program or know how it works? Open Source provides the source code for its programs so that anyone can use, modify or learn how to write those programs themselves. Visit the GNU source code repositories to download the source.
Education
Study at Harvard, Stanford or MIT - Open edX provides free online courses from Harvard, MIT, Columbia, UC Berkeley and other top Universities. Hundreds of courses for almost all major subjects and course levels. Open edx also offers some paid courses and selected certifications.
Linux Manual Pages - A man or manual page is a form of software documentation found on Linux/Unix operating systems. Topics covered include computer programs (including library and system calls), formal standards and conventions, and even abstract concepts.
