2022-174

In the Non-linear preferential attachment, the preferential attachment probability becomes $\mathrm{\Pi }(k)\sim k^{\alpha }$. For a starting network with 1 node, approximately how many nodes we have to add on the network for it to achieve $k_{max}=100$, considering the cases where $\alpha$ is 0.5, 1, and 1.5, respectively?

1. 22026 nodes; 10000 nodes; 100 nodes, respectively
2. 1024 nodes; 1000 nodes; 100 nodes respectively
3. 22026 nodes; 10000 nodes; 200 nodes, respectively
4. 1024 nodes; 1000 nodes; 200 nodes, respectively
5. None of the above.

Original idea by: Pedro Henrique Di Francia Rosso