graph(n) Tcl Data Structures graph(n)
NAME
graph - Create and manipulate directed graph objects
SYNOPSIS
package require Tcl 8.2
package require struct ??2.00??
::::struct::::graph ?graphName? ?==::==asdeserialize 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 get arc key
graphName arc getall arc ?pattern?
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 source arc
graphName arc target arc
graphName arc unset arc key
graphName arcs ?-key key? ?-value value? ?-filter cmdprefix?
?-in-out-adj-inner-embedding nodelist?
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 ?child?
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 nodelist?
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? -com-
mand cmd
DESCRIPTION
A directed graph is a structure containing two collections of elements,
called nodes and arcs respectively, together with a relation ("connec-
tivity") 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 adja-
cent. 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 for-
mer 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 ver-
sion 2.0, due to backward incompatible changes in the API of this mod-
ule. Please read the section Changes for 2.00 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? ?==::==asdeserialize 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 initial-
ized 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
::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]
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]
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 associ-
ated 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 noth-
ing 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 speci-
fied a list containing all arcs is returned. Restrictions can
limit the list of returned arcs based on the nodes that are con-
nected 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 con-
text 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 -embed-
ded are applied first. After that the restrictions set via -key (and
-value) are applied. Any restriction set through -filter is applied
last.
graphName lappend key value
Appends a value (as a list) to one of the keyed values associ-
ated 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 speci-
fied 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 associ-
ated 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 dic-
tionary. 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 serial-
ized. 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 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 ref-
erence 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 seri-
alization, 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 con-
sistency requirement for the serialization.
[3] 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.
# 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.
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? -com-
mand cmd
Perform a breadth-first or depth-first walk of the graph start-
ing 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.
Changes for 2.00
The following noteworthy changes have occurred:
[1] The API for accessing attributes and their values has been sim-
plified.
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 argu-
ment 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, deseri-
alize, ==, 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 cri-
terium.
KEYWORDS
cgraph, graph, serialization
COPYRIGHT
Copyright (c) 2002 Andreas Kupries
struct 2.0 graph(n)
|
