1struct::graph(n) Tcl Data Structures struct::graph(n)
2______________________________________________________________________________
6
8 struct::graph - Create and manipulate directed graph objects
9
11 package require Tcl 8.4
12 package require struct::graph ?2.4.1?
14 package require struct::list ?1.5?
16 package require struct::set ?2.2.3?
18 ::struct::graph ?graphName? ?=|:=|as|deserialize source?
20 graphName option ?arg arg ...?
22 graphName = sourcegraph
24 graphName --> destgraph
26 graphName append key value
28 graphName deserialize serialization
30 graphName destroy
32 graphName arc append arc key value
34 graphName arc attr key
36 graphName arc attr key -arcs list
38 graphName arc attr key -glob globpattern
40 graphName arc attr key -regexp repattern
42 graphName arc delete arc ?arc ...?
44 graphName arc exists arc
46 graphName arc flip arc
48 graphName arc get arc key
50 graphName arc getall arc ?pattern?
52 graphName arc getunweighted
54 graphName arc getweight arc
56 graphName arc keys arc ?pattern?
58 graphName arc keyexists arc key
60 graphName arc insert start end ?child?
62 graphName arc lappend arc key value
64 graphName arc rename arc newname
66 graphName arc set arc key ?value?
68 graphName arc setunweighted ?weight?
70 graphName arc setweight arc weight
72 graphName arc unsetweight arc
74 graphName arc hasweight arc
76 graphName arc source arc
78 graphName arc target arc
80 graphName arc nodes arc
82 graphName arc move-source arc newsource
84 graphName arc move-target arc newtarget
86 graphName arc move arc newsource newtarget
88 graphName arc unset arc key
90 graphName arc weights
92 graphName arcs ?-key key? ?-value value? ?-filter cmdprefix?
94 ?-in|-out|-adj|-inner|-embedding node node...?
95 graphName lappend key value
97 graphName node append node key value
99 graphName node attr key
101 graphName node attr key -nodes list
103 graphName node attr key -glob globpattern
105 graphName node attr key -regexp repattern
107 graphName node degree ?-in|-out? node
109 graphName node delete node ?node...?
111 graphName node exists node
113 graphName node get node key
115 graphName node getall node ?pattern?
117 graphName node keys node ?pattern?
119 graphName node keyexists node key
121 graphName node insert ?node...?
123 graphName node lappend node key value
125 graphName node opposite node arc
127 graphName node rename node newname
129 graphName node set node key ?value?
131 graphName node unset node key
133 graphName nodes ?-key key? ?-value value? ?-filter cmdprefix?
135 ?-in|-out|-adj|-inner|-embedding node node...?
136 graphName get key
138 graphName getall ?pattern?
140 graphName keys ?pattern?
142 graphName keyexists key
144 graphName serialize ?node...?
146 graphName set key ?value?
148 graphName swap node1 node2
150 graphName unset key
152 graphName walk node ?-order order? ?-type type? ?-dir direction? -com‐
154 mand cmd
155______________________________________________________________________________
157
159 A directed graph is a structure containing two collections of elements,
160 called nodes and arcs respectively, together with a relation ("connec‐
161 tivity") that places a general structure upon the nodes and arcs.
162 Each arc is connected to two nodes, one of which is called the source
164 and the other the target. This imposes a direction upon the arc, which
165 is said to go from the source to the target. It is allowed that source
166 and target of an arc are the same node. Such an arc is called a loop.
167 Whenever a node is either the source or target of an arc both are said
168 to be adjacent. This extends into a relation between nodes, i.e. if two
169 nodes are connected through at least one arc they are said to be adja‐
170 cent too.
171 Each node can be the source and target for any number of arcs. The for‐
173 mer are called the outgoing arcs of the node, the latter the incoming
174 arcs of the node. The number of arcs in either set is called the in-
175 degree resp. the out-degree of the node.
176 In addition to maintaining the node and arc relationships, this graph
178 implementation allows any number of named attributes to be associated
179 with the graph itself, and each node or arc.
180 Note: The major version of the package struct has been changed to ver‐
182 sion 2.0, due to backward incompatible changes in the API of this mod‐
183 ule. Please read the section Changes for 2.0 for a full list of all
184 changes, incompatible and otherwise.
185 Note: A C-implementation of the command can be had from the location
187 http://www.purl.org/NET/schlenker/tcl/cgraph. See also
188 http://wiki.tcl.tk/cgraph. This implementation uses a bit less memory
189 than the tcl version provided here directly, and is faster. Its support
190 is limited to versions of the package before 2.0.
191 As of version 2.2 of this package a critcl based C implementation is
193 available from here as well. This implementation however requires Tcl
194 8.4 to run.
195 The main command of the package is:
197 ::struct::graph ?graphName? ?=|:=|as|deserialize source?
199 The command creates a new graph object with an associated global
200 Tcl command whose name is graphName. This command may be used
201 to invoke various operations on the graph. It has the following
202 general form:
203 graphName option ?arg arg ...?
205 Option and the args determine the exact behavior of the
206 command.
207 If graphName is not specified a unique name will be generated by the
209 package itself. If a source is specified the new graph will be initial‐
210 ized to it. For the operators =, :=, and as the source argument is
211 interpreted as the name of another graph object, and the assignment
212 operator = will be executed. For the operator deserialize the source is
213 a serialized graph object and deserialize will be executed.
214 In other words
216 ::struct::graph mygraph = b
220 is equivalent to
223 ::struct::graph mygraph
227 mygraph = b
228 and
231 ::struct::graph mygraph deserialize $b
235 is equivalent to
238 ::struct::graph mygraph
242 mygraph deserialize $b
243 The following commands are possible for graph objects:
246 graphName = sourcegraph
248 This is the assignment operator for graph objects. It copies the
249 graph contained in the graph object sourcegraph over the graph
250 data in graphName. The old contents of graphName are deleted by
251 this operation.
252 This operation is in effect equivalent to
254 graphName deserialize [sourcegraph serialize]
258 The operation assumes that the sourcegraph provides the method serial‐
261 ize and that this method returns a valid graph serialization.
262 graphName --> destgraph
264 This is the reverse assignment operator for graph objects. It
265 copies the graph contained in the graph object graphName over
266 the graph data in the object destgraph. The old contents of
267 destgraph are deleted by this operation.
268 This operation is in effect equivalent to
270 destgraph deserialize [graphName serialize]
274 The operation assumes that the destgraph provides the method deserial‐
277 ize and that this method takes a graph serialization.
278 graphName append key value
280 Appends a value to one of the keyed values associated with the
281 graph. Returns the new value given to the attribute key.
282 graphName deserialize serialization
284 This is the complement to serialize. It replaces the graph data
285 in graphName with the graph described by the serialization
286 value. The old contents of graphName are deleted by this opera‐
287 tion.
288 graphName destroy
290 Destroys the graph, including its storage space and associated
291 command.
292 graphName arc append arc key value
294 Appends a value to one of the keyed values associated with an
295 arc. Returns the new value given to the attribute key.
296 graphName arc attr key
298 graphName arc attr key -arcs list
300 graphName arc attr key -glob globpattern
302 graphName arc attr key -regexp repattern
304 This method retrieves the value of the attribute named key, for
305 all arcs in the graph (matching the restriction specified via
306 one of the possible options) and having the specified attribute.
307 The result is a dictionary mapping from arc names to the value
309 of attribute key at that arc. Arcs not having the attribute
310 key, or not passing a specified restriction, are not listed in
311 the result.
312 The possible restrictions are:
314 -arcs The value is a list of arcs. Only the arcs mentioned in
316 this list are searched for the attribute.
317 -glob The value is a glob pattern. Only the arcs in the graph
319 whose names match this pattern are searched for the
320 attribute.
321 -regexp
323 The value is a regular expression. Only the arcs in the
324 graph whose names match this pattern are searched for the
325 attribute.
326 graphName arc delete arc ?arc ...?
329 Remove the specified arcs from the graph.
330 graphName arc exists arc
332 Return true if the specified arc exists in the graph.
333 graphName arc flip arc
335 Reverses the direction of the named arc, i.e. the source and
336 target nodes of the arc are exchanged with each other.
337 graphName arc get arc key
339 Returns the value associated with the key key for the arc.
340 graphName arc getall arc ?pattern?
342 Returns a dictionary (suitable for use with [array set]) for the
343 arc. If the pattern is specified only the attributes whose
344 names match the pattern will be part of the returned dictionary.
345 The pattern is a glob pattern.
346 graphName arc getunweighted
348 Returns a list containing the names of all arcs in the graph
349 which have no weight associated with them.
350 graphName arc getweight arc
352 Returns the weight associated with the arc. Throws an error if
353 the arc has no weight associated with it.
354 graphName arc keys arc ?pattern?
356 Returns a list of keys for the arc. If the pattern is specified
357 only the attributes whose names match the pattern will be part
358 of the returned list. The pattern is a glob pattern.
359 graphName arc keyexists arc key
361 Return true if the specified key exists for the arc.
362 graphName arc insert start end ?child?
364 Insert an arc named child into the graph beginning at the node
365 start and ending at the node end. If the name of the new arc is
366 not specified the system will generate a unique name of the form
367 arcx.
368 graphName arc lappend arc key value
370 Appends a value (as a list) to one of the keyed values associ‐
371 ated with an arc. Returns the new value given to the attribute
372 key.
373 graphName arc rename arc newname
375 Renames the arc arc to newname. An error is thrown if either the
376 arc does not exist, or a arc with name newname does exist. The
377 result of the command is the new name of the arc.
378 graphName arc set arc key ?value?
380 Set or get one of the keyed values associated with an arc. An
381 arc may have any number of keyed values associated with it. If
382 value is not specified, this command returns the current value
383 assigned to the key; if value is specified, this command assigns
384 that value to the key, and returns that value.
385 graphName arc setunweighted ?weight?
387 Sets the weight of all arcs without a weight to weight. Returns
388 the empty string as its result. If not present weight defaults
389 to 0.
390 graphName arc setweight arc weight
392 Sets the weight of the arc to weight. Returns weight.
393 graphName arc unsetweight arc
395 Removes the weight of the arc, if present. Does nothing other‐
396 wise. Returns the empty string.
397 graphName arc hasweight arc
399 Determines if the arc has a weight associated with it. The
400 result is a boolean value, True if a weight is defined, and
401 False otherwise.
402 graphName arc source arc
404 Return the node the given arc begins at.
405 graphName arc target arc
407 Return the node the given arc ends at.
408 graphName arc nodes arc
410 Return the nodes the given arc begins and ends at, as a two-ele‐
411 ment list.
412 graphName arc move-source arc newsource
414 Changes the source node of the arc to newsource. It can be said
415 that the arc rotates around its target node.
416 graphName arc move-target arc newtarget
418 Changes the target node of the arc to newtarget. It can be said
419 that the arc rotates around its source node.
420 graphName arc move arc newsource newtarget
422 Changes both source and target nodes of the arc to newsource,
423 and newtarget resp.
424 graphName arc unset arc key
426 Remove a keyed value from the arc arc. The method will do noth‐
427 ing if the key does not exist.
428 graphName arc weights
430 Returns a dictionary whose keys are the names of all arcs which
431 have a weight associated with them, and the values are these
432 weights.
433 graphName arcs ?-key key? ?-value value? ?-filter cmdprefix?
435 ?-in|-out|-adj|-inner|-embedding node node...?
436 Returns a list of arcs in the graph. If no restriction is speci‐
437 fied a list containing all arcs is returned. Restrictions can
438 limit the list of returned arcs based on the nodes that are con‐
439 nected by the arc, on the keyed values associated with the arc,
440 or both. A general filter command can be used as well. The
441 restrictions that involve connected nodes take a variable number
442 of nodes as argument, specified after the name of the restric‐
443 tion itself.
444 The restrictions imposed by either -in, -out, -adj, -inner, or
446 -embedded are applied first. Specifying more than one of them is
447 illegal.
448 After that the restrictions set via -key (and -value) are
450 applied. Specifying more than one -key (and -value) is illegal.
451 Specifying -value alone, without -key is illegal as well.
452 Any restriction set through -filter is applied last. Specifying
454 more than one -filter is illegal.
455 Coming back to the restrictions based on a set of nodes, the
457 command recognizes the following switches:
458 -in Return a list of all arcs whose target is one of the
460 nodes in the set of nodes. I.e. it computes the union of
461 all incoming arcs of the nodes in the set.
462 -out Return a list of all arcs whose source is one of the
464 nodes in the set of nodes. I.e. it computes the union of
465 all outgoing arcs of the nodes in the set.
466 -adj Return a list of all arcs adjacent to at least one of the
468 nodes in the set. This is the union of the nodes returned
469 by -in and -out.
470 -inner Return a list of all arcs which are adjacent to two of
472 the nodes in the set. This is the set of arcs in the sub‐
473 graph spawned by the specified nodes.
474 -embedding
476 Return a list of all arcs adjacent to exactly one of the
477 nodes in the set. This is the set of arcs connecting the
478 subgraph spawned by the specified nodes to the rest of
479 the graph.
480 -key key
482 Limit the list of arcs that are returned to those arcs
483 that have an associated key key.
484 -value value
486 This restriction can only be used in combination with
487 -key. It limits the list of arcs that are returned to
488 those arcs whose associated key key has the value value.
489 -filter cmdrefix
491 Limit the list of arcs that are returned to those arcs
492 that pass the test. The command in cmdprefix is called
493 with two arguments, the name of the graph object, and the
494 name of the arc in question. It is executed in the con‐
495 text of the caller and has to return a boolean value.
496 Arcs for which the command returns false are removed from
497 the result list before it is returned to the caller.
498 graphName lappend key value
500 Appends a value (as a list) to one of the keyed values associ‐
501 ated with the graph. Returns the new value given to the
502 attribute key.
503 graphName node append node key value
505 Appends a value to one of the keyed values associated with an
506 node. Returns the new value given to the attribute key.
507 graphName node attr key
509 graphName node attr key -nodes list
511 graphName node attr key -glob globpattern
513 graphName node attr key -regexp repattern
515 This method retrieves the value of the attribute named key, for
516 all nodes in the graph (matching the restriction specified via
517 one of the possible options) and having the specified attribute.
518 The result is a dictionary mapping from node names to the value
520 of attribute key at that node. Nodes not having the attribute
521 key, or not passing a specified restriction, are not listed in
522 the result.
523 The possible restrictions are:
525 -nodes The value is a list of nodes. Only the nodes mentioned in
527 this list are searched for the attribute.
528 -glob The value is a glob pattern. Only the nodes in the graph
530 whose names match this pattern are searched for the
531 attribute.
532 -regexp
534 The value is a regular expression. Only the nodes in the
535 graph whose names match this pattern are searched for the
536 attribute.
537 graphName node degree ?-in|-out? node
540 Return the number of arcs adjacent to the specified node. If one
541 of the restrictions -in or -out is given only the incoming resp.
542 outgoing arcs are counted.
543 graphName node delete node ?node...?
545 Remove the specified nodes from the graph. All of the nodes'
546 arcs will be removed as well to prevent unconnected arcs.
547 graphName node exists node
549 Return true if the specified node exists in the graph.
550 graphName node get node key
552 Return the value associated with the key key for the node.
553 graphName node getall node ?pattern?
555 Returns a dictionary (suitable for use with [array set]) for the
556 node. If the pattern is specified only the attributes whose
557 names match the pattern will be part of the returned dictionary.
558 The pattern is a glob pattern.
559 graphName node keys node ?pattern?
561 Returns a list of keys for the node. If the pattern is speci‐
562 fied only the attributes whose names match the pattern will be
563 part of the returned list. The pattern is a glob pattern.
564 graphName node keyexists node key
566 Return true if the specified key exists for the node.
567 graphName node insert ?node...?
569 Insert one or more nodes into the graph. The new nodes have no
570 arcs connected to them. If no node is specified one node will be
571 inserted, and the system will generate a unique name of the form
572 nodex for it.
573 graphName node lappend node key value
575 Appends a value (as a list) to one of the keyed values associ‐
576 ated with an node. Returns the new value given to the attribute
577 key.
578 graphName node opposite node arc
580 Return the node at the other end of the specified arc, which has
581 to be adjacent to the given node.
582 graphName node rename node newname
584 Renames the node node to newname. An error is thrown if either
585 the node does not exist, or a node with name newname does exist.
586 The result of the command is the new name of the node.
587 graphName node set node key ?value?
589 Set or get one of the keyed values associated with a node. A
590 node may have any number of keyed values associated with it. If
591 value is not specified, this command returns the current value
592 assigned to the key; if value is specified, this command assigns
593 that value to the key.
594 graphName node unset node key
596 Remove a keyed value from the node node. The method will do
597 nothing if the key does not exist.
598 graphName nodes ?-key key? ?-value value? ?-filter cmdprefix?
600 ?-in|-out|-adj|-inner|-embedding node node...?
601 Return a list of nodes in the graph. Restrictions can limit the
602 list of returned nodes based on neighboring nodes, or based on
603 the keyed values associated with the node. The restrictions that
604 involve neighboring nodes have a list of nodes as argument,
605 specified after the name of the restriction itself.
606 The possible restrictions are the same as for method arcs. The
608 exact meanings change slightly, as they operate on nodes instead
609 of arcs. The command recognizes:
610 -in Return a list of all nodes with at least one outgoing arc
612 ending in a node found in the specified set of nodes.
613 Alternatively specified as the set of source nodes for
614 the -in arcs of the node set. The incoming neighbours.
615 -out Return a list of all nodes with at least one incoming arc
617 starting in a node found in the specified set of nodes.
618 Alternatively specified as the set of target nodes for
619 the -out arcs of the node set. The outgoing neighbours.
620 -adj This is the union of the nodes returned by -in and -out.
622 The neighbours.
623 -inner The set of neighbours (see -adj above) which are also in
625 the set of nodes. I.e. the intersection between the set
626 of nodes and the neighbours per -adj.
627 -embedding
629 The set of neighbours (see -adj above) which are not in
630 the set of nodes. I.e. the difference between the neigh‐
631 bours as per -adj, and the set of nodes.
632 -key key
634 Limit the list of nodes that are returned to those nodes
635 that have an associated key key.
636 -value value
638 This restriction can only be used in combination with
639 -key. It limits the list of nodes that are returned to
640 those nodes whose associated key key has the value value.
641 -filter cmdrefix
643 Limit the list of nodes that are returned to those nodes
644 that pass the test. The command in cmdprefix is called
645 with two arguments, the name of the graph object, and the
646 name of the node in question. It is executed in the con‐
647 text of the caller and has to return a boolean value.
648 Nodes for which the command returns false are removed
649 from the result list before it is returned to the caller.
650 graphName get key
652 Return the value associated with the key key for the graph.
653 graphName getall ?pattern?
655 Returns a dictionary (suitable for use with [array set]) for the
656 whole graph. If the pattern is specified only the attributes
657 whose names match the pattern will be part of the returned dic‐
658 tionary. The pattern is a glob pattern.
659 graphName keys ?pattern?
661 Returns a list of keys for the whole graph. If the pattern is
662 specified only the attributes whose names match the pattern will
663 be part of the returned list. The pattern is a glob pattern.
664 graphName keyexists key
666 Return true if the specified key exists for the whole graph.
667 graphName serialize ?node...?
669 This method serializes the sub-graph spanned up by the nodes. In
670 other words it returns a tcl value completely describing that
671 graph. If no nodes are specified the whole graph will be serial‐
672 ized. This allows, for example, the transfer of graph objects
673 (or parts thereof) over arbitrary channels, persistence, etc.
674 This method is also the basis for both the copy constructor and
675 the assignment operator.
676 The result of this method has to be semantically identical over
678 all implementations of the graph interface. This is what will
679 enable us to copy graph data between different implementations
680 of the same interface.
681 The result is a list containing a multiple of three items, plus
683 one! In other words, '[llength $serial] % 3 == 1'. Valid values
684 include 1, 4, 7, ...
685 The last element of the list is a dictionary containing the
687 attributes associated with the whole graph. Regarding the other
688 elements; each triple consists of
689 [1] The name of the node to be described,
691 [2] A dictionary containing the attributes associated with
693 the node,
694 [3] And a list describing all the arcs starting at that node.
696 The elements of the arc list are lists containing three or four ele‐
698 ments each, i.e.
699 [1] The name of the arc described by the element,
701 [2] A reference to the destination node of the arc. This ref‐
703 erence is an integer number given the index of that node
704 in the main serialization list. As that it is greater
705 than or equal to zero, less than the length of the seri‐
706 alization, and a multiple of three. Note: For internal
707 consistency no arc name may be used twice, whether in the
708 same node, or at some other node. This is a global con‐
709 sistency requirement for the serialization.
710 [3] And a dictionary containing the attributes associated
712 with the arc.
713 [4] The weight associated with the arc. This value is
715 optional. Its non-presence means that the arc in question
716 has no weight associated with it.
717 Note: This information is new, compared to the serializa‐
719 tion of graph 2.3 and earlier. By making it an optional
720 element the new format is maximally compatible with the
721 old. This means that any graph not using weights will
722 generate a serialization which is still understood by the
723 older graph package. A serialization will not be under‐
724 stood any longer by the older packages if, and only if
725 the graph it was generated from actually has arcs with
726 weights.
727 For all attribute dictionaries they keys are the names of the
729 attributes, and the values are the values for each name.
730 Note: The order of the nodes in the serialization has no relevance, nor
732 has the order of the arcs per node.
733 # A possible serialization for the graph structure
736 #
737 # d -----> %2
738 # / ^ \\
739 # / / \\
740 # / b \\
741 # / / \\
742 # %1 <- a - %0 e
743 # ^ \\ /
744 # \\ c /
745 # \\ \\ /
746 # \\ v v
747 # f ------ %3
748 # is
749 #
750 # %3 {} {{f 6 {}}} %0 {} {{a 6 {}} {b 9 {}} {c 0 {}}} %1 {} {{d 9 {}}} %2 {} {{e 0 {}}} {}
751 #
752 # This assumes that the graph has neither attribute data nor weighted arcs.
753 graphName set key ?value?
757 Set or get one of the keyed values associated with a graph. A
758 graph may have any number of keyed values associated with it. If
759 value is not specified, this command returns the current value
760 assigned to the key; if value is specified, this command assigns
761 that value to the key.
762 graphName swap node1 node2
764 Swap the position of node1 and node2 in the graph.
765 graphName unset key
767 Remove a keyed value from the graph. The method will do nothing
768 if the key does not exist.
769 graphName walk node ?-order order? ?-type type? ?-dir direction? -com‐
771 mand cmd
772 Perform a breadth-first or depth-first walk of the graph start‐
773 ing at the node node going in either the direction of outgoing
774 or opposite to the incoming arcs.
775 The type of walk, breadth-first or depth-first, is determined by
777 the value of type; bfs indicates breadth-first, dfs indicates
778 depth-first. Depth-first is the default.
779 The order of the walk, pre-order, post-order or both-order is
781 determined by the value of order; pre indicates pre-order, post
782 indicates post-order, both indicates both-order. Pre-order is
783 the default. Pre-order walking means that a node is visited
784 before any of its neighbors (as defined by the direction, see
785 below). Post-order walking means that a parent is visited after
786 any of its neighbors. Both-order walking means that a node is
787 visited before and after any of its neighbors. The combination
788 of a breadth-first walk with post- or both-order is illegal.
789 The direction of the walk is determined by the value of dir;
791 backward indicates the direction opposite to the incoming arcs,
792 forward indicates the direction of the outgoing arcs.
793 As the walk progresses, the command cmd will be evaluated at
795 each node, with the mode of the call (enter or leave) and values
796 graphName and the name of the current node appended. For a pre-
797 order walk, all nodes are entered, for a post-order all nodes
798 are left. In a both-order walk the first visit of a node enters
799 it, the second visit leaves it.
800
802 The following noteworthy changes have occurred:
803 [1] The API for accessing attributes and their values has been sim‐
805 plified.
806 All functionality regarding the default attribute "data" has
808 been removed. This default attribute does not exist anymore. All
809 accesses to attributes have to specify the name of the attribute
810 in question. This backward incompatible change allowed us to
811 simplify the signature of all methods handling attributes.
812 Especially the flag -key is not required anymore, even more, its
814 use is now forbidden. Please read the documentation for the arc
815 and node methods set, get, getall, unset, append, lappend,
816 keyexists and keys for a description of the new API's.
817 [2] The methods keys and getall now take an optional pattern argu‐
819 ment and will return only attribute data for keys matching this
820 pattern.
821 [3] Arcs and nodes can now be renamed. See the documentation for the
823 methods arc rename and node rename.
824 [4] The structure has been extended with API's for the serialization
826 and deserialization of graph objects, and a number of operations
827 based on them (graph assignment, copy construction).
828 Please read the documentation for the methods serialize, deseri‐
830 alize, =, and -->, and the documentation on the construction of
831 graph objects.
832 Beyond the copying of whole graph objects these new API's also
834 enable the transfer of graph objects over arbitrary channels and
835 for easy persistence.
836 [5] A new method, attr, was added to both arc and node allowing the
838 query and retrieval of attribute data without regard to arc and
839 node relationships.
840 [6] Both methods arcs and nodes have been extended with the ability
842 to select arcs and nodes based on an arbitrary filtering cri‐
843 terium.
844
846 This document, and the package it describes, will undoubtedly contain
847 bugs and other problems. Please report such in the category struct ::
848 graph of the Tcllib Trackers [http://core.tcl.tk/tcllib/reportlist].
849 Please also report any ideas for enhancements you may have for either
850 package and/or documentation.
851 When proposing code changes, please provide unified diffs, i.e the out‐
853 put of diff -u.
854 Note further that attachments are strongly preferred over inlined
856 patches. Attachments can be made by going to the Edit form of the
857 ticket immediately after its creation, and then using the left-most
858 button in the secondary navigation bar.
859
861 adjacent, arc, cgraph, degree, edge, graph, loop, neighbour, node,
862 serialization, subgraph, vertex
863
865 Data structures
866
868 Copyright (c) 2002-2009 Andreas Kupries <andreas_kupries@users.sourceforge.net>
869tcllib 2.4.1 struct::graph(n)