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 ?2.4.3?
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-de‐
175 gree 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 in‐
211 terpreted as the name of another graph object, and the assignment oper‐
212 ator = will be executed. For the operator deserialize the source is a
213 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 at‐
320 tribute.
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 re‐
400 sult is a boolean value, True if a weight is defined, and False
401 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 re‐
441 strictions 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 -embedding are applied first. Specifying more than one of them
447 is illegal.
448 After that the restrictions set via -key (and -value) are ap‐
450 plied. 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 Attention: After the above options any word with a leading dash
482 which is not a valid option is treated as a node name instead of
483 an invalid option to error out on. This condition holds until
484 either a valid option terminates the list of nodes, or the end
485 of the command is reached, whichever comes first.
486 The remaining filter options are:
488 -key key
491 Limit the list of arcs that are returned to those arcs
492 that have an associated key key.
493 -value value
495 This restriction can only be used in combination with
496 -key. It limits the list of arcs that are returned to
497 those arcs whose associated key key has the value value.
498 -filter cmdrefix
500 Limit the list of arcs that are returned to those arcs
501 that pass the test. The command in cmdprefix is called
502 with two arguments, the name of the graph object, and the
503 name of the arc in question. It is executed in the con‐
504 text of the caller and has to return a boolean value.
505 Arcs for which the command returns false are removed from
506 the result list before it is returned to the caller.
507 graphName lappend key value
509 Appends a value (as a list) to one of the keyed values associ‐
510 ated with the graph. Returns the new value given to the attri‐
511 bute key.
512 graphName node append node key value
514 Appends a value to one of the keyed values associated with an
515 node. Returns the new value given to the attribute key.
516 graphName node attr key
518 graphName node attr key -nodes list
520 graphName node attr key -glob globpattern
522 graphName node attr key -regexp repattern
524 This method retrieves the value of the attribute named key, for
525 all nodes in the graph (matching the restriction specified via
526 one of the possible options) and having the specified attribute.
527 The result is a dictionary mapping from node names to the value
529 of attribute key at that node. Nodes not having the attribute
530 key, or not passing a specified restriction, are not listed in
531 the result.
532 The possible restrictions are:
534 -nodes The value is a list of nodes. Only the nodes mentioned in
536 this list are searched for the attribute.
537 -glob The value is a glob pattern. Only the nodes in the graph
539 whose names match this pattern are searched for the at‐
540 tribute.
541 -regexp
543 The value is a regular expression. Only the nodes in the
544 graph whose names match this pattern are searched for the
545 attribute.
546 graphName node degree ?-in|-out? node
549 Return the number of arcs adjacent to the specified node. If one
550 of the restrictions -in or -out is given only the incoming resp.
551 outgoing arcs are counted.
552 graphName node delete node ?node...?
554 Remove the specified nodes from the graph. All of the nodes'
555 arcs will be removed as well to prevent unconnected arcs.
556 graphName node exists node
558 Return true if the specified node exists in the graph.
559 graphName node get node key
561 Return the value associated with the key key for the node.
562 graphName node getall node ?pattern?
564 Returns a dictionary (suitable for use with [array set]) for the
565 node. If the pattern is specified only the attributes whose
566 names match the pattern will be part of the returned dictionary.
567 The pattern is a glob pattern.
568 graphName node keys node ?pattern?
570 Returns a list of keys for the node. If the pattern is speci‐
571 fied only the attributes whose names match the pattern will be
572 part of the returned list. The pattern is a glob pattern.
573 graphName node keyexists node key
575 Return true if the specified key exists for the node.
576 graphName node insert ?node...?
578 Insert one or more nodes into the graph. The new nodes have no
579 arcs connected to them. If no node is specified one node will be
580 inserted, and the system will generate a unique name of the form
581 nodex for it.
582 graphName node lappend node key value
584 Appends a value (as a list) to one of the keyed values associ‐
585 ated with an node. Returns the new value given to the attribute
586 key.
587 graphName node opposite node arc
589 Return the node at the other end of the specified arc, which has
590 to be adjacent to the given node.
591 graphName node rename node newname
593 Renames the node node to newname. An error is thrown if either
594 the node does not exist, or a node with name newname does exist.
595 The result of the command is the new name of the node.
596 graphName node set node key ?value?
598 Set or get one of the keyed values associated with a node. A
599 node may have any number of keyed values associated with it. If
600 value is not specified, this command returns the current value
601 assigned to the key; if value is specified, this command assigns
602 that value to the key.
603 graphName node unset node key
605 Remove a keyed value from the node node. The method will do
606 nothing if the key does not exist.
607 graphName nodes ?-key key? ?-value value? ?-filter cmdprefix?
609 ?-in|-out|-adj|-inner|-embedding node node...?
610 Return a list of nodes in the graph. Restrictions can limit the
611 list of returned nodes based on neighboring nodes, or based on
612 the keyed values associated with the node. The restrictions that
613 involve neighboring nodes have a list of nodes as argument,
614 specified after the name of the restriction itself.
615 The possible restrictions are the same as for method arcs. Note
617 that while the exact meanings change slightly, as they operate
618 on nodes instead of arcs, the general behaviour is the same, es‐
619 pecially when it comes to the handling of words with a leading
620 dash in node lists.
621 The command recognizes:
623 -in Return a list of all nodes with at least one outgoing arc
625 ending in a node found in the specified set of nodes. Al‐
626 ternatively specified as the set of source nodes for the
627 -in arcs of the node set. The incoming neighbours.
628 -out Return a list of all nodes with at least one incoming arc
630 starting in a node found in the specified set of nodes.
631 Alternatively specified as the set of target nodes for
632 the -out arcs of the node set. The outgoing neighbours.
633 -adj This is the union of the nodes returned by -in and -out.
635 The neighbours.
636 -inner The set of neighbours (see -adj above) which are also in
638 the set of nodes. I.e. the intersection between the set
639 of nodes and the neighbours per -adj.
640 -embedding
642 The set of neighbours (see -adj above) which are not in
643 the set of nodes. I.e. the difference between the neigh‐
644 bours as per -adj, and the set of nodes.
645 -key key
647 Limit the list of nodes that are returned to those nodes
648 that have an associated key key.
649 -value value
651 This restriction can only be used in combination with
652 -key. It limits the list of nodes that are returned to
653 those nodes whose associated key key has the value value.
654 -filter cmdrefix
656 Limit the list of nodes that are returned to those nodes
657 that pass the test. The command in cmdprefix is called
658 with two arguments, the name of the graph object, and the
659 name of the node in question. It is executed in the con‐
660 text of the caller and has to return a boolean value.
661 Nodes for which the command returns false are removed
662 from the result list before it is returned to the caller.
663 graphName get key
665 Return the value associated with the key key for the graph.
666 graphName getall ?pattern?
668 Returns a dictionary (suitable for use with [array set]) for the
669 whole graph. If the pattern is specified only the attributes
670 whose names match the pattern will be part of the returned dic‐
671 tionary. The pattern is a glob pattern.
672 graphName keys ?pattern?
674 Returns a list of keys for the whole graph. If the pattern is
675 specified only the attributes whose names match the pattern will
676 be part of the returned list. The pattern is a glob pattern.
677 graphName keyexists key
679 Return true if the specified key exists for the whole graph.
680 graphName serialize ?node...?
682 This method serializes the sub-graph spanned up by the nodes. In
683 other words it returns a tcl value completely describing that
684 graph. If no nodes are specified the whole graph will be serial‐
685 ized. This allows, for example, the transfer of graph objects
686 (or parts thereof) over arbitrary channels, persistence, etc.
687 This method is also the basis for both the copy constructor and
688 the assignment operator.
689 The result of this method has to be semantically identical over
691 all implementations of the graph interface. This is what will
692 enable us to copy graph data between different implementations
693 of the same interface.
694 The result is a list containing a multiple of three items, plus
696 one! In other words, '[llength $serial] % 3 == 1'. Valid values
697 include 1, 4, 7, ...
698 The last element of the list is a dictionary containing the at‐
700 tributes associated with the whole graph. Regarding the other
701 elements; each triple consists of
702 [1] The name of the node to be described,
704 [2] A dictionary containing the attributes associated with
706 the node,
707 [3] And a list describing all the arcs starting at that node.
709 The elements of the arc list are lists containing three or four ele‐
711 ments each, i.e.
712 [1] The name of the arc described by the element,
714 [2] A reference to the destination node of the arc. This ref‐
716 erence is an integer number given the index of that node
717 in the main serialization list. As that it is greater
718 than or equal to zero, less than the length of the seri‐
719 alization, and a multiple of three. Note: For internal
720 consistency no arc name may be used twice, whether in the
721 same node, or at some other node. This is a global con‐
722 sistency requirement for the serialization.
723 [3] And a dictionary containing the attributes associated
725 with the arc.
726 [4] The weight associated with the arc. This value is op‐
728 tional. Its non-presence means that the arc in question
729 has no weight associated with it.
730 Note: This information is new, compared to the serializa‐
732 tion of graph 2.3 and earlier. By making it an optional
733 element the new format is maximally compatible with the
734 old. This means that any graph not using weights will
735 generate a serialization which is still understood by the
736 older graph package. A serialization will not be under‐
737 stood any longer by the older packages if, and only if
738 the graph it was generated from actually has arcs with
739 weights.
740 For all attribute dictionaries they keys are the names of the at‐
742 tributes, and the values are the values for each name.
743 Note: The order of the nodes in the serialization has no relevance, nor
745 has the order of the arcs per node.
746 # A possible serialization for the graph structure
749 #
750 # d -----> %2
751 # / ^ \
752 # / / \
753 # / b \
754 # / / \
755 # %1 <- a - %0 e
756 # ^ \\ /
757 # \\ c /
758 # \\ \\ /
759 # \\ v v
760 # f ------ %3
761 # is
762 #
763 # %3 {} {{f 6 {}}} %0 {} {{a 6 {}} {b 9 {}} {c 0 {}}} %1 {} {{d 9 {}}} %2 {} {{e 0 {}}} {}
764 #
765 # This assumes that the graph has neither attribute data nor weighted arcs.
766 graphName set key ?value?
770 Set or get one of the keyed values associated with a graph. A
771 graph may have any number of keyed values associated with it. If
772 value is not specified, this command returns the current value
773 assigned to the key; if value is specified, this command assigns
774 that value to the key.
775 graphName swap node1 node2
777 Swap the position of node1 and node2 in the graph.
778 graphName unset key
780 Remove a keyed value from the graph. The method will do nothing
781 if the key does not exist.
782 graphName walk node ?-order order? ?-type type? ?-dir direction? -com‐
784 mand cmd
785 Perform a breadth-first or depth-first walk of the graph start‐
786 ing at the node node going in either the direction of outgoing
787 or opposite to the incoming arcs.
788 The type of walk, breadth-first or depth-first, is determined by
790 the value of type; bfs indicates breadth-first, dfs indicates
791 depth-first. Depth-first is the default.
792 The order of the walk, pre-order, post-order or both-order is
794 determined by the value of order; pre indicates pre-order, post
795 indicates post-order, both indicates both-order. Pre-order is
796 the default. Pre-order walking means that a node is visited be‐
797 fore any of its neighbors (as defined by the direction, see be‐
798 low). Post-order walking means that a parent is visited after
799 any of its neighbors. Both-order walking means that a node is
800 visited before and after any of its neighbors. The combination
801 of a breadth-first walk with post- or both-order is illegal.
802 The direction of the walk is determined by the value of dir;
804 backward indicates the direction opposite to the incoming arcs,
805 forward indicates the direction of the outgoing arcs.
806 As the walk progresses, the command cmd will be evaluated at
808 each node, with the mode of the call (enter or leave) and values
809 graphName and the name of the current node appended. For a pre-
810 order walk, all nodes are entered, for a post-order all nodes
811 are left. In a both-order walk the first visit of a node enters
812 it, the second visit leaves it.
813
815 The following noteworthy changes have occurred:
816 [1] The API for accessing attributes and their values has been sim‐
818 plified.
819 All functionality regarding the default attribute "data" has
821 been removed. This default attribute does not exist anymore. All
822 accesses to attributes have to specify the name of the attribute
823 in question. This backward incompatible change allowed us to
824 simplify the signature of all methods handling attributes.
825 Especially the flag -key is not required anymore, even more, its
827 use is now forbidden. Please read the documentation for the arc
828 and node methods set, get, getall, unset, append, lappend,
829 keyexists and keys for a description of the new API's.
830 [2] The methods keys and getall now take an optional pattern argu‐
832 ment and will return only attribute data for keys matching this
833 pattern.
834 [3] Arcs and nodes can now be renamed. See the documentation for the
836 methods arc rename and node rename.
837 [4] The structure has been extended with API's for the serialization
839 and deserialization of graph objects, and a number of operations
840 based on them (graph assignment, copy construction).
841 Please read the documentation for the methods serialize, deseri‐
843 alize, =, and -->, and the documentation on the construction of
844 graph objects.
845 Beyond the copying of whole graph objects these new API's also
847 enable the transfer of graph objects over arbitrary channels and
848 for easy persistence.
849 [5] A new method, attr, was added to both arc and node allowing the
851 query and retrieval of attribute data without regard to arc and
852 node relationships.
853 [6] Both methods arcs and nodes have been extended with the ability
855 to select arcs and nodes based on an arbitrary filtering cri‐
856 terium.
857
859 This document, and the package it describes, will undoubtedly contain
860 bugs and other problems. Please report such in the category struct ::
861 graph of the Tcllib Trackers [http://core.tcl.tk/tcllib/reportlist].
862 Please also report any ideas for enhancements you may have for either
863 package and/or documentation.
864 When proposing code changes, please provide unified diffs, i.e the out‐
866 put of diff -u.
867 Note further that attachments are strongly preferred over inlined
869 patches. Attachments can be made by going to the Edit form of the
870 ticket immediately after its creation, and then using the left-most
871 button in the secondary navigation bar.
872
874 adjacent, arc, cgraph, degree, edge, graph, loop, neighbour, node, se‐
875 rialization, subgraph, vertex
876
878 Data structures
879
881 Copyright (c) 2002-2009,2019 Andreas Kupries <andreas_kupries@users.sourceforge.net>
882tcllib 2.4.3 struct::graph(n)