We study a sequential learning model featuring a network of naive agents with Gaussian information structures. Agents wrongly believe their predecessors act solely on private information, so they neglect redundancies among observed actions. We provide a simple linear formula expressing agents' actions in terms of network paths and use this formula to characterize the set of networks where naive agents eventually learn correctly. This characterization shows that, on all networks where later agents observe more than one neighbor, there exist disproportionately influential early agents who can cause herding on incorrect actions. Going beyond existing social-learning results, we compute the probability of such mislearning exactly. This allows us to compare likelihoods of incorrect herding, and hence expected welfare losses, across network structures. The probability of mislearning increases when link densities are higher and when networks are more integrated. In partially segregated networks, divergent early signals can lead to persistent disagreement between groups.