In analyzing peer effects in a linear-in-means framework, identifying who interacts with whom is crucial. This suggests the need to collect detailed network data. However, taking a cue from AddHealth, many data-collection efforts only permit respondents to list up to a maximum number of links, leading to censoring and mismeasurement of peer groups. Within a linear-in-means framework, I document the extent of bias due to censoring analytically and by simulation. I then demonstrate that censoring-induced bias is present in empirical applications using data from AddHealth and an experiment in rural Nepal. After documenting the bias, I provide strategies to recover consistent estimates and discuss limitations of these strategies. This paper provides important contributions to the literature on the design of network surveys as well as estimation of peer effects in the presence of data limitations.