[3] This preferential attachment model relies on nodes keeping memory of previous neighbors up to the current time.
[1][4] In real social networks individuals exhibit a tendency to re-connect with past contacts (ex.
In a simple model for this mechanism, a node's propensity to establish a new link can be characterized solely by
In these models an infected node's chances of connecting to new contacts diminishes as their size of their social circle
grows leading to a limiting effect on the growth of n. The result is strong ties with a node's early contacts and consequently the weakening of the diffusion of the contagion.