struct::graph(n)              Tcl Data Structures             struct::graph(n)



______________________________________________________________________________

NAME
       struct::graph - Create and manipulate directed graph objects

SYNOPSIS
       package require Tcl  8.4

       package require struct::graph  ?2.4?

       package require struct::list  ?1.5?

       package require struct::set  ?2.2.3?

       ::struct::graph ?graphName? ?=|:=|as|deserialize source?

       graphName option ?arg arg ...?

       graphName = sourcegraph

       graphName --> destgraph

       graphName append key value

       graphName deserialize serialization

       graphName destroy

       graphName arc append arc key value

       graphName arc attr key

       graphName arc attr key -arcs list

       graphName arc attr key -glob globpattern

       graphName arc attr key -regexp repattern

       graphName arc delete arc ?arc ...?

       graphName arc exists arc

       graphName arc flip arc

       graphName arc get arc key

       graphName arc getall arc ?pattern?

       graphName arc getunweighted

       graphName arc getweight arc

       graphName arc keys arc ?pattern?

       graphName arc keyexists arc key

       graphName arc insert start end ?child?

       graphName arc lappend arc key value

       graphName arc rename arc newname

       graphName arc set arc key ?value?

       graphName arc setunweighted ?weight?

       graphName arc setweight arc weight

       graphName arc unsetweight arc

       graphName arc hasweight arc

       graphName arc source arc

       graphName arc target arc

       graphName arc nodes arc

       graphName arc move-source arc newsource

       graphName arc move-target arc newtarget

       graphName arc move arc newsource newtarget

       graphName arc unset arc key

       graphName arc weights

       graphName arcs ?-key key? ?-value value? ?-filter cmdprefix?
       ?-in|-out|-adj|-inner|-embedding node node...?

       graphName lappend key value

       graphName node append node key value

       graphName node attr key

       graphName node attr key -nodes list

       graphName node attr key -glob globpattern

       graphName node attr key -regexp repattern

       graphName node degree ?-in|-out? node

       graphName node delete node ?node...?

       graphName node exists node

       graphName node get node key

       graphName node getall node ?pattern?

       graphName node keys node ?pattern?

       graphName node keyexists node key

       graphName node insert ?node...?

       graphName node lappend node key value

       graphName node opposite node arc

       graphName node rename node newname

       graphName node set node key ?value?

       graphName node unset node key

       graphName nodes ?-key key? ?-value value? ?-filter cmdprefix?
       ?-in|-out|-adj|-inner|-embedding node node...?

       graphName get key

       graphName getall ?pattern?

       graphName keys ?pattern?

       graphName keyexists key

       graphName serialize ?node...?

       graphName set key ?value?

       graphName swap node1 node2

       graphName unset key

       graphName walk node ?-order order? ?-type type? ?-dir direction?
       -command cmd

_________________________________________________________________

DESCRIPTION
       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 outgoing arcs of the node, the latter the
       incoming arcs 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 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. 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|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 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



                  graphName deserialize [sourcegraph serialize]


       The operation assumes that the sourcegraph provides the method
       serialize and that this method returns a valid graph serialization.

       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]


       The operation assumes that the destgraph provides the method
       deserialize and that this method takes a graph serialization.

       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 the graph data
              in graphName with the graph described by the serialization
              value. The old contents of graphName are deleted by this
              operation.

       graphName destroy
              Destroys the graph, including its storage space and associated
              command.

       graphName arc append arc key value
              Appends a value to one of the keyed values associated with an
              arc. Returns the new value given to the attribute key.

       graphName arc attr key

       graphName arc attr key -arcs list

       graphName arc attr key -glob globpattern

       graphName arc attr key -regexp repattern
              This method retrieves the value of the attribute named key, for
              all arcs in the graph (matching the restriction specified via
              one of the possible options) and having the specified attribute.

              The result is a dictionary mapping from arc names to the value
              of attribute key at that arc.  Arcs not having the attribute
              key, or not passing a specified restriction, are not listed in
              the result.

              The possible restrictions are:

              -arcs  The value is a list of arcs. Only the arcs mentioned in
                     this list are searched for the attribute.

              -glob  The value is a glob pattern. Only the arcs in the graph
                     whose names match this pattern are searched for the
                     attribute.

              -regexp
                     The value is a regular expression. Only the arcs in the
                     graph whose names match this pattern are searched for the
                     attribute.


       graphName arc delete arc ?arc ...?
              Remove the specified arcs from the graph.

       graphName arc exists arc
              Return true if the specified arc exists in the graph.

       graphName arc flip arc
              Reverses the direction of the named arc, i.e. the source and
              target nodes of the arc are exchanged with each other.

       graphName arc get arc key
              Returns 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 getunweighted
              Returns a list containing the names of all arcs in the graph
              which have no weight associated with them.

       graphName arc getweight arc
              Returns the weight associated with the arc. Throws an error if
              the arc has no weight associated with it.

       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 setunweighted ?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.

       graphName arc setweight arc weight
              Sets the weight of the arc to weight. Returns weight.

       graphName arc unsetweight arc
              Removes the weight of the arc, if present. Does nothing
              otherwise. Returns the empty string.

       graphName arc hasweight arc
              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.

       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 nodes arc
              Return the nodes the given arc begins and ends at, as a two-
              element list.

       graphName arc move-source arc newsource
              Changes the source node of the arc to newsource. It can be said
              that the arc rotates around its target node.

       graphName arc move-target arc newtarget
              Changes the target node of the arc to newtarget. It can be said
              that the arc rotates around its source node.

       graphName arc move arc newsource newtarget
              Changes both source and target nodes of the arc to newsource,
              and newtarget resp.

       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 arc weights
              Returns a dictionary whose keys are the names of all arcs which
              have a weight associated with them, and the values are these
              weights.

       graphName arcs ?-key key? ?-value value? ?-filter cmdprefix?
       ?-in|-out|-adj|-inner|-embedding node node...?
              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
              -embedded 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.

              -key key
                     Limit the list of arcs that are returned to those arcs
                     that have an associated key key.

              -value value
                     This restriction can only be used in combination with
                     -key. It limits the list of arcs that are returned to
                     those arcs whose associated key key has the value value.

              -filter cmdrefix
                     Limit the list of arcs that are returned to those arcs
                     that pass the test. The command in cmdprefix is called
                     with two arguments, the name of the graph object, and the
                     name of the arc in question. It is executed in the
                     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.

       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 attr key

       graphName node attr key -nodes list

       graphName node attr key -glob globpattern

       graphName node attr key -regexp repattern
              This method retrieves the value of the attribute named key, for
              all nodes in the graph (matching the restriction specified via
              one of the possible options) and having the specified attribute.

              The result is a dictionary mapping from node names to the value
              of attribute key at that node.  Nodes not having the attribute
              key, or not passing a specified restriction, are not listed in
              the result.

              The possible restrictions are:

              -nodes The value is a list of nodes. Only the nodes mentioned in
                     this list are searched for the attribute.

              -glob  The value is a glob pattern. Only the nodes in the graph
                     whose names match this pattern are searched for the
                     attribute.

              -regexp
                     The value is a regular expression. Only the nodes in the
                     graph whose names match this pattern are searched for the
                     attribute.


       graphName node degree ?-in|-out? node
              Return the number of arcs adjacent to the specified node. If one
              of the restrictions -in or -out is given only the incoming resp.
              outgoing arcs are counted.

       graphName node delete node ?node...?
              Remove the specified nodes from the graph.  All of the nodes'
              arcs will be removed as well to prevent unconnected arcs.

       graphName node exists node
              Return true if the specified node exists in the graph.

       graphName node get node key
              Return the value associated with the key key for the node.

       graphName node getall node ?pattern?
              Returns a dictionary (suitable for use with [array set]) for the
              node.  If the pattern is specified only the attributes whose
              names match the pattern will be part of the returned dictionary.
              The pattern is a glob pattern.

       graphName node keys node ?pattern?
              Returns a list of keys for the node.  If the pattern is
              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 ?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.

       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? ?-filter cmdprefix?
       ?-in|-out|-adj|-inner|-embedding node node...?
              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
              exact meanings change slightly, as they operate on nodes instead
              of arcs. 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 incoming neighbours.

              -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 outgoing neighbours.

              -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.

              -key key
                     Limit the list of nodes that are returned to those nodes
                     that have an associated key key.

              -value value
                     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.

              -filter cmdrefix
                     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.

       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

              [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.



       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 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.

CHANGES FOR 2.0
       The following noteworthy changes have occurred:

       [1]    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.

       [2]    The methods keys and getall now take an optional pattern
              argument and will return only attribute data for keys matching
              this pattern.

       [3]    Arcs and nodes can now be renamed. See the documentation for the
              methods arc rename and node rename.

       [4]    The structure has been extended with API's for the serialization
              and deserialization of graph objects, and a number of operations
              based on them (graph assignment, copy construction).

              Please read the documentation for the methods serialize,
              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.

       [5]    A new method, attr, was added to both arc and node allowing the
              query and retrieval of attribute data without regard to arc and
              node relationships.

       [6]    Both methods arcs and nodes have been extended with the ability
              to select arcs and nodes based on an arbitrary filtering
              criterium.

BUGS, IDEAS, FEEDBACK
       This document, and the package it describes, will undoubtedly contain
       bugs and other problems.  Please report such in the category struct ::
       graph of the Tcllib SF Trackers
       [http://sourceforge.net/tracker/?group_id=12883].  Please also report
       any ideas for enhancements you may have for either package and/or
       documentation.

KEYWORDS
       adjacent, arc, cgraph, degree, edge, graph, loop, neighbour, node,
       serialization, subgraph, vertex

CATEGORY
       Data structures

COPYRIGHT
       Copyright (c) 2002-2009 Andreas Kupries <andreas_kupries@users.sourceforge.net>




struct                                2.4                     struct::graph(n)
