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GraphTheory

  

HasSelfLoop

  

NumberOfSelfLoops

  

SelfLoops

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

HasSelfLoop(G)

HasSelfLoop(G, v)

NumberOfSelfLoops(G)

SelfLoops(G)

Parameters

G

-

graph

v

-

vertex of the graph

Description

• 

If v is a vertex of the graph, HasSelfLoop(G,v) returns true if the graph G has an edge or arc v to itself, and false otherwise.

• 

The NumberOfSelfLoops(G) command returns the number of self-loops in G.

• 

The SelfLoops(G) command returns a set of self-loops in G.

• 

Because the data structure for a graph is an array of sets of neighbors, the test for self-loop existence checks each neighbor set and the cost is O(n) where n is the number of vertices.

Examples

withGraphTheory:

GGraph1,2,2,3,3,3,3,4,4,1

GGraph 1: a directed unweighted graph with 4 vertices, 4 arc(s), and 1 self-loop(s)

(1)

HasSelfLoopG,2

false

(2)

HasSelfLoopG,3

true

(3)

NumberOfSelfLoopsG

1

(4)

Compatibility

• 

The GraphTheory[HasSelfLoop], GraphTheory[NumberOfSelfLoops] and GraphTheory[SelfLoops] commands were introduced in Maple 2020.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

Graph

HighlightEdges