What does $\sum_{i/k_i = k}$ mean in the equation below?

Question

I was reading chapter 5 of Dynamical Processes on Complex Networks, which discusses the Ising model, where I encountered the following equation for the average magnetization of the class of nodes with degree k: $$\langle \sigma \rangle_k = \frac{1}{N_k}\sum_{i/k_i = k} \langle \sigma_i \rangle$$

I'm particularly confused by the notation $$\sum_{i/k_i = k}$$

Can anyone explain what this means?

Answer 1

$$\sum\limits_{i\mid k_i=k} a_i,$$ also written $$\sum\limits_{i: k_i=k} a_i,$$ means to sum $a_i$ over indices $i$ such that $k_i=k$.

To make it clearer that the formula is an average, I probably would have first defined $N_k = \{i \in N: k_i = k\}$ as the set of nodes with degree $k$ and then used the expression $$\langle \sigma \rangle_k = \frac{1}{|N_k|}\sum_{i\in N_k} \langle \sigma_i \rangle$$