We elicit social networks among students in an Italian high school either by measuring the complete network in an incentive-compatible way or by using a truncated elicitation of at most five links. We find that truncation undercounts weak links by up to 90% but only moderately undercounts the time spent with strong friends. We use simulations to demonstrate that the measurement error induced by censoring might be particularly significant when studying phenomena such as social learning which are often thought to operate along weak ties. We then discuss how a modified network elicitation protocol might be able to reduce measurement error.