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

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?

$$\sum\limits_{i\mid k_i=k} a_i,$$ 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 $$\langle \sigma \rangle_k = \frac{1}{|N_k|}\sum_{i\in N_k} \langle \sigma_i \rangle$$
• / and | are equivalent notations in this case, then? – EJoshuaS - Reinstate Monica Apr 13 at 2:18
• Yes, but $\mid$ and $:$ are more common. – RobPratt Apr 13 at 2:19
• If $i/k_i=k$ for integers, then it seems that $k\mid i$, rather than $i\mid k$. Does dynamical systems really standardly reverse things/misuse $/$ in this way? – Mark S. Apr 13 at 10:47
• @MarkS. there is no division here. The $/$ or $\mid$ indicates such that here. Better notation would have been $i\in N: k_i=k$. – RobPratt Apr 13 at 12:48