Hello,
I'm trying to tackle this problem, but I must admit that I'm stuck: I don't really know how we should compute the coefficient value, can we reduce it to its expected value its average value ? It's not clear to me when we are allowed to do so and where we are not considering the exercice's statement.
Also, I don't have an "intuitive" result for this computation, meaning I'm not sure what my output should/will represent (related to this post's question).
A few things to note here that may help you get started: first, the clustering coefficient of the WS model without shortcuts is an entirely deterministic problem (it's just an n-cycle with a lattice of additional edges to nearby nodes), so there is nothing to take an expectation over. Second, by symmetry, the clustering coefficient of every node is the same, so you can just focus on an arbitrary node at the center, and use the definition in the class notes. It's about finding a good way of counting triangles...
Exercice 3 - clustering coefficient computation
Hello,
I'm trying to tackle this problem, but I must admit that I'm stuck: I don't really know how we should compute the coefficient value, can we reduce it to its expected value its average value ? It's not clear to me when we are allowed to do so and where we are not considering the exercice's statement.
Also, I don't have an "intuitive" result for this computation, meaning I'm not sure what my output should/will represent (related to this post's question).
Thanks a lot !
A few things to note here that may help you get started: first, the clustering coefficient of the WS model without shortcuts is an entirely deterministic problem (it's just an n-cycle with a lattice of additional edges to nearby nodes), so there is nothing to take an expectation over. Second, by symmetry, the clustering coefficient of every node is the same, so you can just focus on an arbitrary node at the center, and use the definition in the class notes. It's about finding a good way of counting triangles...
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