A graph $G(V,E)$ is growing with following rule:
At every time step $t$, $An_t$ nodes are added to the graph. When choosing the node to which the new node connects to, we assume that the probability $P$ that a new node will be connected to some node $i$ depends on the degree $k_i$ of node $i$ , such that $P \propto \frac{k_i}{\sum_j k_j}$.
What is the rate of change of the degree $k_i$ of the node $i$?