Need Help with capturing path count in a network problem

Hi, I need help in counting the number of times a path is used in a network problem. For the provided diagram a component is connected with other components. Lets say component C1 is connected to Component C6 in 3 steps I want to give points to connections C1-C2, C2-C3 and C3-C6 and store it in 6 by 6 matrix (C1 C2 C3 C4 C5 C6 vs C1 C2 C3 C4 C5 C6). I appreciate any help. Thanks

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