This book constitutes the refereed proceedings of the First International Workshop on Graph Learning in Medical Imaging, GLMI 2019, held in conjunction with MICCAI 2019 in Shenzhen, China, in October 2019. The 21 full papers presented were carefully reviewed and selected from 42 submissions. The papers focus on major trends and challenges of graph learning in medical imaging and present original work aimed to identify new cutting-edge techniques and their applications in medical imaging.