graph (3)

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 www.purl.org/NET/schlenker/tcl/cgraph. See also 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 Trackers [core.tcl.tk/tcllib/reportlist] 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>