The research community of Geographic Information Systems and Science (GIS) has been growing rapidly during the last two decades. Little attention has been paid to understanding its geography, structure and evolution. Taking a new organizational perspective, this article aims to fill the knowledge gap by analyzing collaboration and citation networks between GIS research organizations, including academic institutions, government agencies, businesses, and others. These two networks are analyzed in geographical and bibliographical spaces, respectively, to discover characteristic distributions and structures. The results show an uneven geographic distribution of GIS research organizations, and clustered spatial interactions between them. Both collaboration and citation networks exhibit typical "scale-free" structures, which came into being around the year 2000 and have remained to the present. Further, the GIS research community is composed of 11 cohesive sub-groups, with each having a clear hub-spoke structure and a few highly connected organizations as leaders. These results shed light on the overall picture of the GIS research community, and offer a reference system that stimulates further exploration.