# Cycles in Silver Connecting Two Barns Test Data?

I’m currently looking at the test data from 2021 December Silver Problem 2 (Connecting Two Barns, data found here) and the problem states that

It is guaranteed that there is at most one path between any two fields

I believe that this should imply that there are no cycles in the graph of fields connected by the bidirectional paths (please correct me if I’m wrong here). However, when I look at the data from test case #2, the first sub-test case contains the following edges:

8 5
11 9
7 2
3 11
3 4
3 1
7 11
6 3
10 9
2 10
8 9
5 10
9 2
5 2
3 5

When I looked closer at this, I noticed that it contained the edges:

• 11 9
• 7 2
• 7 11
• 10 9
• 2 10

implying the cycle 11-7-2-10-9-11, which means that there are two paths between nodes 11 and 9:

• 11 → 7 → 2 → 10 → 9
• 11 → 9

Doesn’t this contradict the problem statement, or am I misinterpreting something? Thanks!

The problem statement isn’t wrong, but it would be less confusing if “path” was replaced with “edge” everywhere.