This data, grsg_lcp_ThiessenPoly_mst4, is one of five hierarchical delineations of greater sage-grouse population structure. The data represent Thiessen polygons of graph constructs (least-cost path minimum spanning tree [LCP-MST]) that defined our population structure of sage-grouse breeding sites in the western United States. This data was developed by applying dispersal and genetic rules to decompose the fully connected population structure (graph) into the product presented here. Understanding wildlife population structure and connectivity can help managers identify conservation strategies, as structure can facilitate the study of population changes and habitat connectivity can provide information on dispersal and biodiversity. We developed an approach to define hierarchical population structure (in other words, demarcation of subpopulations) using graph theory (in other words, connectivity) from an amalgamation of biological inferences encompassing dispersal capabilities based on movements and genetic flow, seasonal habitat conditions, and functional processes (for example, selection of habitat at multiple scales) affecting movements. We applied our approach to greater sage-grouse (Centrocercus urophasianus), an upland gamebird species of conservation concern in western United States. We defined sage-grouse population structure by creating a cost surface, informed from functional processes of habitat characteristics to account for the resistance of inter-patch movements, and developing least-cost paths between breeding habitat sites (leks). The least-cost paths were combined into a multi-path graph construct for which we then used information on potential connectivity (dispersal distances) and functional connectivity (permeability of fragmented landscapes based on selection preferences) to decompose the graph into structures of subpopulations.