This paper introduces and tests a novel methodology for measuring networks. Rather than collecting data to observe a network or several networks in full, which is typically costly or impossible, we randomly sample a portion of individuals in the network and estimate the network based on the sampled individuals' perceptions on all possible ties. We find the methodology produces accurate estimates of social structure and network level indices in five different datasets. In order to illustrate the performance of our approach we compare its results with the traditional roster and ego network methods of data collection. Across all five datasets, our methodology outperforms these standard social network data collection methods. We offer ideas on applications of our methodology, and find it especially promising in cross-network settings.