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 outgoingarcs of
the node, the latter the incomingarcs 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 Changesfor2.0 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|deserializesource?
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:
graphNameoption ?argarg...?
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
graphNamedeserialize [sourcegraphserialize]
The operation assumes that the sourcegraph provides the method serialize and that this method returns a
valid graph serialization.
graphName-->destgraph
This is the reverseassignment 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
destgraphdeserialize [graphNameserialize]
The operation assumes that the destgraph provides the method deserialize and that this method takes a
graph serialization.
graphNameappendkeyvalue
Appends a value to one of the keyed values associated with the graph. Returns the new value given
to the attribute key.
graphNamedeserializeserialization
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.
graphNamedestroy
Destroys the graph, including its storage space and associated command.
graphNamearcappendarckeyvalue
Appends a value to one of the keyed values associated with an arc. Returns the new value given to
the attribute key.
graphNamearcattrkeygraphNamearcattrkey-arcslistgraphNamearcattrkey-globglobpatterngraphNamearcattrkey-regexprepattern
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.
graphNamearcdeletearc ?arc ...?
Remove the specified arcs from the graph.
graphNamearcexistsarc
Return true if the specified arc exists in the graph.
graphNamearcfliparc
Reverses the direction of the named arc, i.e. the source and target nodes of the arc are exchanged
with each other.
graphNamearcgetarckey
Returns the value associated with the key key for the arc.
graphNamearcgetallarc ?pattern?
Returns a dictionary (suitable for use with [arrayset]) 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.
graphNamearcgetunweighted
Returns a list containing the names of all arcs in the graph which have no weight associated with
them.
graphNamearcgetweightarc
Returns the weight associated with the arc. Throws an error if the arc has no weight associated
with it.
graphNamearckeysarc ?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.
graphNamearckeyexistsarckey
Return true if the specified key exists for the arc.
graphNamearcinsertstartend ?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.
graphNamearclappendarckeyvalue
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.
graphNamearcrenamearcnewname
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.
graphNamearcsetarckey ?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.
graphNamearcsetunweighted ?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.
graphNamearcsetweightarcweight
Sets the weight of the arc to weight. Returns weight.
graphNamearcunsetweightarc
Removes the weight of the arc, if present. Does nothing otherwise. Returns the empty string.
graphNamearchasweightarc
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.
graphNamearcsourcearc
Return the node the given arc begins at.
graphNamearctargetarc
Return the node the given arc ends at.
graphNamearcnodesarc
Return the nodes the given arc begins and ends at, as a two-element list.
graphNamearcmove-sourcearcnewsource
Changes the source node of the arc to newsource. It can be said that the arc rotates around its
target node.
graphNamearcmove-targetarcnewtarget
Changes the target node of the arc to newtarget. It can be said that the arc rotates around its
source node.
graphNamearcmovearcnewsourcenewtarget
Changes both source and target nodes of the arc to newsource, and newtarget resp.
graphNamearcunsetarckey
Remove a keyed value from the arc arc. The method will do nothing if the key does not exist.
graphNamearcweights
Returns a dictionary whose keys are the names of all arcs which have a weight associated with
them, and the values are these weights.
graphNamearcs ?-key key? ?-value value? ?-filter cmdprefix? ?-in|-out|-adj|-inner|-embedding nodenode...?
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:
-keykey
Limit the list of arcs that are returned to those arcs that have an associated key key.
-valuevalue
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.
-filtercmdrefix
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.
graphNamelappendkeyvalue
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.
graphNamenodeappendnodekeyvalue
Appends a value to one of the keyed values associated with an node. Returns the new value given to
the attribute key.
graphNamenodeattrkeygraphNamenodeattrkey-nodeslistgraphNamenodeattrkey-globglobpatterngraphNamenodeattrkey-regexprepattern
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.
graphNamenodedegree ?-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.
graphNamenodedeletenode ?node...?
Remove the specified nodes from the graph. All of the nodes' arcs will be removed as well to
prevent unconnected arcs.
graphNamenodeexistsnode
Return true if the specified node exists in the graph.
graphNamenodegetnodekey
Return the value associated with the key key for the node.
graphNamenodegetallnode ?pattern?
Returns a dictionary (suitable for use with [arrayset]) 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.
graphNamenodekeysnode ?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.
graphNamenodekeyexistsnodekey
Return true if the specified key exists for the node.
graphNamenodeinsert ?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.
graphNamenodelappendnodekeyvalue
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.
graphNamenodeoppositenodearc
Return the node at the other end of the specified arc, which has to be adjacent to the given node.
graphNamenoderenamenodenewname
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.
graphNamenodesetnodekey ?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.
graphNamenodeunsetnodekey
Remove a keyed value from the node node. The method will do nothing if the key does not exist.
graphNamenodes ?-key key? ?-value value? ?-filter cmdprefix? ?-in|-out|-adj|-inner|-embedding nodenode...?
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 incomingneighbours.
-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 outgoingneighbours.
-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.
-keykey
Limit the list of nodes that are returned to those nodes that have an associated key key.
-valuevalue
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.
-filtercmdrefix
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.
graphNamegetkey
Return the value associated with the key key for the graph.
graphNamegetall ?pattern?
Returns a dictionary (suitable for use with [arrayset]) 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.
graphNamekeys ?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.
graphNamekeyexistskey
Return true if the specified key exists for the whole graph.
graphNameserialize ?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.
graphNamesetkey ?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.
graphNameswapnode1node2
Swap the position of node1 and node2 in the graph.
graphNameunsetkey
Remove a keyed value from the graph. The method will do nothing if the key does not exist.
graphNamewalknode ?-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.
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