Eq. 3.5 and others

[luismieryteran]

It seems to me that in the evolution of pairs, eg. in eq 3.5b, the sum over k should be k != i, j. Currently, it is only restricted to k != i. I think this applies to several pair equations, such as 3.5, 3.6, 3.7.

[joelmiller]

Thank you for your report.

You are correct that k!= i and k!=j in these sums.

However, in this case, we are looking at terms like <S_i S_j I_k>, meaning a central node j connected to nodes i and k. If k=j, this would mean node j is connected to itself. We have been assuming that this case does not occur, so any case in which the central index were the same as either of the others would have to be 0. We will explore how to best clarify this in the second edition.

[luismieryteran]

Thanks for the clarification, Joel, excited about the new edition! I am currently going over chapter 3, slowly, and could probably use reminders here and there stating the connectivity assumptions wrt i, j, k.