Diffusion on network

Question

There is not any definition about $\delta_{ij}$ in my print for diffusion on network.What is $\delta_{ij}$?

This is part of my print. $d\phi/dt = C(\sum_jA_{ij}\phi_j-\sum_jA_{ij}\phi_i)=C(\sum A_{ij}\phi_j-d_i\phi_i)=C\sum_j(A_{ij}-\delta_{ij}d_j)\phi_j$

Answer 1

This is the Kronecker delta defined as:

$$\delta_{ij} = \begin{cases} 0 &\text{if } i \neq j, \\ 1 &\text{if } i=j. \end{cases}$$

In this context it is used encode that there's an extra term involving $\phi_i$ that is not there for the other $\phi_j$s.