1. Modify the Preferential Attachment model so that as hubs get more and more attachment requests, they decrease their probability of accepting them. How does this change affect the resultant network?

2. Giant component Another model in the Networks section of the models library is the Giant Component model. This model starts with a group of nodes and then adds random links to them. The giant component is the largest connected subcomponent of this network. One question you might ask is, is there a point at which the giant component size grows quickly? How many links do you have to add for this to occur? Does this value change as you change the number of nodes? What if you want all of the nodes to be in the giant component? How many links do you have to add for this to occur? Run the model several times and examine how many ticks it takes to have all the nodes be part of the giant component. Is there any regularity to this amount of time?