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Name

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

Synopsis

package require Tcl 8.2

package require struct ?1.1.1?

::struct::graph graphName

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Description

The ::struct::graph command creates a new graph object with an associated global Tcl command whose name is graph_Name. 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 resp., 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 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 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 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 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 value «» 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 ?-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. If one of the five possible restrictions is specified only arcs satisfying that restriction are returned. All restrictions involve a list of nodes, specified after the key for 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.

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 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 nodex.

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 value «» 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 ?-in|-out|-adj|-inner|-embedding nodelist? Return a list of nodes in the graph. If no restriction is specified a list containing all nodes is returned. If one of the five possible restrictions is specified only nodes satisfying that restriction are returned. All restrictions involve a list of nodes, specified after the key for 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 swap node1 node2
Swap the position of node1 and node2 in the graph.

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. Depthfirst 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


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