Why is there a distinct fundamental cycle for each edge not in the spanning tree

Question

On wikipedia it says that

Adding just one edge to a spanning tree will create a cycle; such a cycle is called a fundamental cycle. There is a distinct fundamental cycle for each edge not in the spanning tree; thus, there is a one-to-one correspondence between fundamental cycles and edges not in the spanning tree.

What if i have a graph like this

1----2

|    |

3    4

and add edge 3-4

1----2

|    |

3----4

There will be indeed only one new cycle but what if i add 1-4? i will then have 2 more cycles 1-4-3 and 1-4-2.

Where am i wrong ?

i am trying to understand how this formula works

For a connected graph with V vertices, any spanning tree will have V − 1 edges, and thus, a graph of E edges and one of its spanning trees will have E − V + 1 fundamental cycles

Thanks in advance !

Answer 1

1-2-4 is a new fundamental cycle, but 1-3-4 is not a fundamental cycle. (A fundamental cycle will have only one edge not belonging to the original tree.)