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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 $i$?

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    I don't think this is right. If you change the starting graph by doubling every edge, you have twice the edges but the same number of nodes. Your formula $\sum_j k_j=2(1+A)^te_0$ would have twice as many nodes at each generation, but the increase is proportional to the number of nodes.2012-04-14

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