graph(n) 2.0 struct "Tcl Data Structures"
graph - Create and manipulate directed graph objects
package require Tcl 8.2
package require struct ?2.0?
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
| |
::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 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? ?-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. 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.
- 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 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? ?-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
restriction as defined for 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.
| |
# 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? -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.
cgraph, graph, serialization
Copyright © 2002 Andreas Kupries <andreas_kupries@users.sourceforge.net>