We study the asymptotic diameter of the preferential attachment model $\operatorname{ PA}\!_n^{ (m,\delta)}$ with parameters $m \ge 2$ and $\delta > 0$. Building on the recent work \cite{ VZ25}, we prove that the diameter of $G_n \sim \operatorname{ PA}\!_n^{ (m,\delta)}$ is $(1+o(1))\log_\nu n$ with high probability, where $\nu$ is the exponential growth rate of the local weak limit of $G_n$. Our result confirms the conjecture in \cite{ VZ25} and closes the remaining gap in understanding the asymptotic diameter of preferential attachment graphs with general parameters $m \ge 1$ and $\delta >-m$. Our proof follows a general recipe that relates the diameter of a random graph to its typical distance, which we expect to have applicability in a broader range of models.
Categories: math.PR math.CO