An apparatus in one embodiment comprises a multi-tier storage system and at least one dispatcher node. The multi-tier storage system comprises at least a front-end storage tier and a back-end storage tier. The at least one dispatcher node is configured to load portions of graph data from the front-end storage tier and the back-end storage tier for graph analytics computations performed at respective ones of a plurality of compute nodes configured for communication with the storage system over at least one network. The multi-tier storage system configured to switch logical connections of respective ones of the compute nodes to the at least one dispatcher node based on progress of graph analytics computations at the compute nodes.