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sage 4.7.2 incorrectly gives girth of 4 on this graph:

sage: H=Graph([(0, 1), (0, 3), (0, 4), (0, 5), (1, 2), (1, 3), (1, 4), (1, 6), (2, 5), (3, 4), (5, 6)])
sage: H.girth()
4

There is a cycle (0,1,3) and sage 4.3 and magma correctly return 3.

sage 4.7.2 incorrectly gives girth of 4 on this graph:

sage: H=Graph([(0, 1), (0, 3), (0, 4), (0, 5), (1, 2), (1, 3), (1, 4), (1, 6), (2, 5), (3, 4), (5, 6)])
sage: H.girth()
4

There is a cycle (0,1,3) and sage 4.3 and magma correctly return 3.

sage 4.7.2 incorrectly gives girth of 4 on this graph:

sage: H=Graph([(0, 1), (0, 3), (0, 4), (0, 5), (1, 2), (1, 3), (1, 4), (1, 6), (2, 5), (3, 4), (5, 6)])
sage: H.girth()
4

There is a cycle (0,1,3) and sage 4.3 and magma correctly return 3.

sage 4.7.2 incorrectly gives girth of 4 on this graph:

sage: H=Graph([(0, 1), (0, 3), (0, 4), (0, 5), (1, 2), (1, 3), (1, 4), (1, 6), (2, 5), (3, 4), (5, 6)])
sage: H.girth()
4

There is a cycle (0,1,3) and sage 4.3 and magma correctly return 3.