# graph(n) 1.2.1 struct "Tcl Data Structures"

## NAME

graph - Create and manipulate directed graph objects

## SYNOPSIS

package require Tcl 8.2
package require struct ?1.2.1?

graphName option ?arg arg ...?
graphName destroy
graphName arc append arc ?-key key? value
graphName arc delete arc ?arc ...?
graphName arc exists arc
graphName arc get arc ?-key key?
graphName arc getall arc
graphName arc keys arc
graphName arc keyexists arc ?-key key?
graphName arc insert start end ?child?
graphName arc lappend arc ?-key key? value
graphName arc set arc ?-key key? ?value?
graphName arc source arc
graphName arc target arc
graphName arc unset arc ?-key key?
graphName arcs ?-key key? ?-value value? ?-in|-out|-adj|-inner|-embedding nodelist?
graphName node append node ?-key key? value
graphName node degree ?-in|-out? node
graphName node delete node ?node ...?
graphName node exists node
graphName node get node ?-key key?
graphName node getall node
graphName node keys node
graphName node keyexists node ?-key key?
graphName node insert ?child?
graphName node lappend node ?-key key? value
graphName node opposite node arc
graphName node set node ?-key key? ?value?
graphName node unset node ?-key key?
graphName nodes ?-key key? ?-value value? ?-in|-out|-adj|-inner|-embedding nodelist?
graphName get ?-key key?
graphName set ?-key key? ?value?
graphName swap node1 node2
graphName unset ?-key key?
graphName walk node ?-order order? ?-type type? ?-dir direction? -command cmd

## DESCRIPTION

The ::struct::graph 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.

A directed graph is a structure containing two collections of elements, called nodes and arcs respectively, together with a relation (&quot;connectivity&quot;) 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 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 edges in either set is called the in- resp. the out-degree of the node.

In addition to maintaining the node and arc relationships, this graph implementation allows any number of keyed values to be associated with each node and arc.

The following commands are possible for graph objects:

graphName destroy
  Destroy the graph, including its storage space and associated command.
graphName arc append arc ?-key key? value
  Appends a value to one of the keyed values associated with an arc. If no key is specified, the key data is assumed.
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 get arc ?-key key?
  Return the value associated with the key key for the arc. If no key is specified, the key data is assumed.
graphName arc getall arc
  Returns a serialized list of key/value pairs (suitable for use with [array set]) for the arc.
graphName arc keys arc
  Returns a list of keys for the arc.
graphName arc keyexists arc ?-key key?
  Return true if the specified key exists for the arc. If no key is specified, the key data is assumed.
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 arc x.
graphName arc lappend arc ?-key key? value
  Appends a value (as a list) to one of the keyed values associated with an arc. If no key is specified, the key data is assumed.
graphName arc set arc ?-key key? ?value?
  Set or get one of the keyed values associated with an arc. If no key is specified, the key data is assumed. Each arc that is added to a graph has the empty string assigned to the key data automatically. 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.
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 unset arc ?-key key?
  Remove a keyed value from the arc arc. If no key is specified, the key data is assumed.
graphName arcs ?-key key? ?-value value? ?-in|-out|-adj|-inner|-embedding nodelist?
  Return 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. The restrictions that involve connected nodes have a list of nodes as argument, specified after the name of the restriction itself.
  -in
    Return a list of all arcs whose target is one of the nodes in the nodelist.
  -out
    Return a list of all arcs whose source is one of the nodes in the nodelist.
  -adj
    Return a list of all arcs adjacent to at least one of the nodes in the nodelist. This is the union of the nodes returned by -in and -out.
  -inner
    Return a list of all arcs adjacent to two of the nodes in the nodelist. 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 nodelist. 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.
graphName node append node ?-key key? value
  Appends a value to one of the keyed values associated with an node. If no key is specified, the key data is assumed.
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 key?
  Return the value associated with the key key for the node. If no key is specified, the key data is assumed.
graphName node getall node
  Returns a serialized list of key/value pairs (suitable for use with [array set]) for the node.
graphName node keys node
  Returns a list of keys for the node.
graphName node keyexists node ?-key key?
  Return true if the specified key exists for the node. If no key is specified, the key data is assumed.
graphName node insert ?child?
  Insert a node named child into the graph. The nodes has no arcs connected to it. If the name of the new child is not specified the system will generate a unique name of the form node x.
graphName node lappend node ?-key key? value
  Appends a value (as a list) to one of the keyed values associated with an node. If no key is specified, the key data is assumed.
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 set node ?-key key? ?value?
  Set or get one of the keyed values associated with a node. If no key is specified, the key data is assumed. Each node that is added to a graph has the empty string assigned to the key data automatically. 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 key?
  Remove a keyed value from the node node. If no key is specified, the key data is assumed.
graphName nodes ?-key key? ?-value value? ?-in|-out|-adj|-inner|-embedding nodelist?
  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 set of nodes to return is computed as the union of all source and target nodes for all the arcs satisfying the restriction as defined for arcs.
graphName get ?-key key?
  Return the value associated with the key key for the graph. If no key is specified, the key data is assumed.
graphName set ?-key key? ?value?
  Set or get one of the keyed values associated with a graph. If no key is specified, the key data is assumed. Each graph has the empty string assigned to the key data automatically. 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 key?
  Remove a keyed value from the graph. If no key is specified, the key data is assumed.
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 bread-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 Bentered, 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.

## KEYWORDS

graph