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







struct::graph - Create and manipulate directed graph objects








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












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:







  

  
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:



  

  
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.

  

  

  
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.

  

  

  
Appends a value to one of the keyed values associated with the
      graph. Returns the new value given to the attribute key.

  

  
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.

  

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

  

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

  

  

  

  

  

  

  

  
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:

  







  

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

  

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

  

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









  

  
Remove the specified arcs from the graph.

  

  
Return true if the specified arc exists in the graph.

  

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

  

  
Returns the value associated with the key key for the
    arc.

  

  
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.

  

  
Returns a list containing the names of all arcs in the graph which have no
      weight associated with them.

  

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

  

  
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.

  

  
Return true if the specified key exists for the arc.

  

  
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.

  

  
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.

  

  
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.

  

  
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.

  

  
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.

  

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

  

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

  

  
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.

  

  
Return the node the given arc begins at.

  

  
Return the node the given arc ends at.

  

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

  

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

  

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

  

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

  

  
Remove a keyed value from the arc arc. The method will do nothing
      if the key does not exist.

  

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

  

  
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:

  







  

  
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.

  

  
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.

  

  
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.

  

  
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.

  

  
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.

  

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

  

  
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.

  

  
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.







  

  
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.

  

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

  

  

  

  

  

  

  

  
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:

  







  

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

  

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

  

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









  

  
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.

  

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

  

  
Return true if the specified node exists in the graph.

  

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

  

  
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.

  

  
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.

  

  
Return true if the specified key exists for the 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.

  

  
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.

  

  
Return the node at the other end of the specified arc, which has to
      be adjacent to the given node.

  

  
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.

  

  
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.

  

  
Remove a keyed value from the node node. The method will do nothing
      if the key does not exist.

  

  
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:

  







  

  
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.

  

  
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.

  

  
This is the union of the nodes returned by -in and -out. The
      neighbours.

  

  
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.

  

  
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.

  

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

  

  
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.

  

  
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.







  

  
Return the value associated with the key key for the graph.

  

  
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.

  

  
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.

  

  
Return true if the specified key exists for the whole graph.

  

  
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.






  

  
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.

  

  
Swap the position of node1 and node2 in the graph.

  

  
Remove a keyed value from the graph. The method will do nothing if the
      key does not exist.

  

  
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.

  










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.










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.








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








Data structures








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








  

    2.4
    struct