# Sample a scale free subnet from random network

I already have a network which is like random complex network. Is there any way I can delete some of nodes and reduce the network into a scale-free network?

I notice there are some methods that can sample a scale-free subnet from a scale-free network. But I have not found anyone sampled a scale-free subnet from a random network.

• I'm not sure what you are aiming at. What is a "scale-free network" for you? – Yuval Filmus Mar 17 '17 at 10:56
• I am trying to sample a subnet whose degree distribution follows a power law. People call that network scale-free network. – James Mar 17 '17 at 14:14

Now, assume your initial random network indeed has high degree nodes. Since it is random, choosing random links in it will often lead to high-degree extremities. Indeed, the probability to pick a degree $$k$$ extremity when you choose a link at random is proportional to $$k$$.