2022-177

Aging can influence the topology of a network.  Denote by $\mathrm{\Pi }(k_i,t-t_i)$ 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 $\mathrm{\Pi }(k_i,t-t_i)\sim k_i(t-t_i{)}^{-\nu }$, 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 $\nu \to -\mathrm{\infty }$ each new node connects to the oldest node.
3. If $\nu >0$ new nodes are encouraged to attach to younger nodes.
4. If $\nu \to \mathrm{\infty }$ each node will connect to its immediate predecessor.
5. None of the above.

Original idea by: Marcelo Silva