2022-177

Aging can influence the topology of a network.  Denote by \( \Pi(k_i,t-t_i) \) the probability of a new node arriving at time \( t \) connecting to node \( i \) of degree \( k_i \), where \( t_i \) is the time node \( i \) was added to the network.  Aging can be modeled by choosing \( \Pi(k_i,t-t_i) \sim k_i(t-t_i)^{-\nu} \), where \( \nu \) is a tunable parameter.  In this case, what is not correct to state regarding the tunable parameter \( \nu \):

1. If \( \nu < 0 \), new nodes will link to older nodes.
2. If \( \nu \rightarrow -\infty \) each new node connects to the oldest node.
3. If \( \nu > 0 \) new nodes are encouraged to attach to younger nodes.
4. If \( \nu \rightarrow \infty \) each node will connect to its immediate predecessor.
5. None of the above.

Original idea by: Marcelo Silva