We quantify the impact of network-based learning and influence on measures of female power and child nutrition in rural India. Empowering women to have greater say in child rearing may generate greater and more lasting benefits to children than nutrition supplementation. While researchers have used proxy reports or correlates like caste to trace networks, we map networks by surveying friends of respondents. We use participation in a women's education program to identify increases in female power, as well as stronger and more diverse networks. We study the ways in which networks affect individuals, namely learning and influence. Finally, we characterize the benefits of using survey data rather than proxies to identify networks. Our results linking networks to child nutrition should also inform child health policy.