Are There Missing Minimal Paths or Cuts?

[brad sue]

Hi,
please I need help with finding the minimal paths and cuts of the attached figure.

Here for the cuts I found: {1,6}, {7,3}, {6,4,2}, {2,5,7}
for the paths I get: {6,7},{1,2,3},{1,2,5,7},{1,4,7}
Do i miss some paths or cut please?

Also i cannot find the an expression for the structure function, using minimal paths and cuts.

Thank you

 

[MarcoD]

I am pretty sure there should be ten paths. What do the labels mean? Are they just labels for the edges or distances?

 

[brad sue]

hi,
the labels are components of the system with their logical connections. how do you know , i need to have 10 paths?

 

[MarcoD]

The graph is strongly connected, there is a path between each two vertices. There are five vertices, so there are 4 paths from an arbitrary vertex to another (not including paths to itself), then from another arbitrary vertex there are 3 paths to other vertices not including the first counted path, etc. 4+3+2+1= 10.