Information updates in multihop networks such as Internet of Things (IoT) and intelligent transportation systems have received significant recent attention. In this paper, we minimize the age of a single information flow in interference-free multihop networks. When preemption is allowed and the packet transmission times are exponentially distributed, we prove that a preemptive last-generated, first-served (LGFS) policy results in smaller age processes across all nodes in the network than any other causal policy (in a stochastic ordering sense). In addition, for the class of new-better-than-used (NBU) distributions, we show that the non-preemptive LGFS policy is within a constant age gap from the optimum average age. In contrast, our numerical result shows that the preemptive LGFS policy can be very far from the optimum for some NBU transmission time distributions. Finally, when preemption is prohibited and the packet transmission times are arbitrarily distributed, the non-preemptive LGFS policy is shown to minimize the age processes across all nodes in the network among all work-conserving policies (again in a stochastic ordering sense). Interestingly, these results hold under quite general conditions, including 1) arbitrary packet generation and arrival times, and 2) for minimizing both the age processes in stochastic ordering and any non-decreasing functional of the age processes.