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.

 

[blue_raver22]

for your question. It seems like you have correctly identified the minimal cuts and paths for the attached figure. However, without knowing the specific structure and properties of the figure, it is difficult to determine if any paths or cuts are missing. It is possible that there could be alternative paths or cuts that could be considered minimal. I would recommend double checking your work and possibly consulting with other experts in the field for their input.

As for finding an expression for the structure function using minimal paths and cuts, this can be a complex and challenging task. The structure function is a mathematical representation of the relationship between nodes in a network or system, and it can vary depending on the specific system being studied. It may be helpful to break down the figure into smaller sub-networks and analyze the paths and cuts within each sub-network to build a larger structure function. Again, consulting with other experts in the field may also be beneficial in finding an appropriate expression for the structure function.