Are the gate and the barrier made of the same material?
No, the gate is made of wood and the barrier is made of metal.
    src        edge_attr  dst
0     0  to the right of    1
1     1               on    5
2     1   to the left of    0
3     1   to the left of    4
4     2   to the left of    3
5     3  to the right of    7
6     3  to the right of    2
7     4  to the right of    5
8     4  to the right of    1
9     5   to the left of    4
10    7   to the left of   11
11    7   to the left of    3
12    9   to the left of   10
13   10  to the right of    9
14   11  to the right of    7