Cycle, detect start:
( 0 1 2 3 )
( 0 1 2 3 0 )

Cycle plus one vertex, start given:
( 0 1 2 3 0 )
( 0 1 2 3 0 1 )

Single edge, detect start:
( 2 )
( 2 3 )

Single edge, directed OUT, detect start:
( 2 )
( 2 3 )

Single edge, directed IN, detect start:
( 2 )
( 3 2 )

Zero edges, start given:
( )
( 2 )