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struct::graph(n) 2.0 "Tcl Data Structures"
struct::graph - Create and manipulate directed graph objects
TABLE OF
CONTENTS
SYNOPSIS
DESCRIPTION
Changes for
2.0
KEYWORDS
COPYRIGHT
package require Tcl 8.2
package require struct::graph ?2.0?
package require struct::list ?1.4?
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
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 edges
in either set is called the in- resp. the
out-degree of the node.
In addition to maintaining the node and arc relationships, this
graph implementation allows any number of keyed values to be
associated with each node and 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.
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 source is interpreted as the
name of another graph object, and the assignment operator
= will be executed. For
deserialize the source is a
serialized graph object and deserialize will be
executed.
In other words
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::struct::graph mygraph = b
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is equivalent to
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::struct::graph mygraph
mygraph = b
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and
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::struct::graph mygraph deserialize $b
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is equivalent to
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::struct::graph mygraph
mygraph deserialize $b
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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
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graphName deserialize [sourcegraph serialize]
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- 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
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destgraph deserialize [graphName serialize]
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- 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 graph data in graphName with the graph
described by the serialization value. The old
contents of graphName are deleted by this
operation.
- graphName
destroy
- Destroy 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
get arc key
- Return 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
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
source arc
- Return the node the given arc begins at.
- graphName arc
target arc
- Return the node the given arc ends at.
- 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 arcs
?-key key? ?-value value?
?-filter cmdprefix?
?-in|-out|-adj|-inner|-embedding nodelist?
- Return 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 have a list of nodes as
argument, specified after the name of the restriction itself.
- -in
- Return a list of all arcs whose target is one of the nodes in
the nodelist.
- -out
- Return a list of all arcs whose source is one of the nodes in
the nodelist.
- -adj
- Return a list of all arcs adjacent to at least one of the nodes
in the nodelist. This is the union of the nodes
returned by -in and -out.
- -inner
- Return a list of all arcs adjacent to two of the nodes in the
nodelist. 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 nodelist. 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.
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. Any
restriction set through -filter is applied last.
Specifying more than one -filter is illegal.
- 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 ?child?
- Insert a node named child into the graph.
The nodes has no arcs connected to it. If the name of the new child
is not specified the system will generate a unique name of the form
nodex.
- 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 nodelist?
- 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 set of nodes to return is computed as
the union of all source and target nodes for all the arcs
satisfying the restrictions as defined for
arcs.
Note that here the -filter command is
applied to the list of nodes, not arcs.
- 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
- The name of the node to be described,
- A dictionary containing the attributes associated with the
node,
- And a list describing all the arcs starting at that node.
The elements of the arc list are lists containing three elements
each, i.e.
- The name of the arc described by the element,
- 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.
- And a dictionary containing the attributes associated with the
arc.
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.
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# 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 no attribute data.
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- 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 bread-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.
The following noteworthy changes have occurred:
- 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.
- The methods keys and getall
now take an optional pattern argument and will return only
attribute data for keys matching this pattern.
- Arcs and nodes can now be renamed. See the documentation for
the methods arc rename and node
rename.
- 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.
- 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.
- Both methods arcs and nodes
have been extended with the ability to select arcs and nodes based
on an arbitrary filtering criterium.
cgraph , graph , serialization
Copyright © 2002 Andreas Kupries
<andreas_kupries@users.sourceforge.net>