Distributed　graph　computing　aims　at　performing　in-depth　analysis　on　large　networks　in　a　parallel　manner.　Iterative　communication　computation　is　an　important　model　to　perform　graph　analysis.　Moreover,　high-efficiency　iterative　communication　computation　is　necessary　for　assuring　the　quality　of　graph　partitioning.　Many　strategies　to　improve　graph　computing　are　usually　based　on　the　hypothesis　of　single　communication　iteration　which　focuses　on　the　optimization　of　load　balance　in　a　single　graph　partitioning　and　the　improvement　of　parallel　granularity　or　communication　manners.　However,　a　graph　in　the　real-world　usually　requires　complex　communication　iterations　to　achieve　good　analysis　results,　which　often　have　the　problems　of　data　and　communication　tilting　and　low　analysis　efficiency.　In　this　paper,　we　propose　a　two-stage　graph　computing　model　with　communication　equilibrium　(TSMCE).　The　model　employs　a　communication-equilibrated　graph　partitioning　strategy　(CEGP)　for　load　balancing　and　a　two-stage　graph　computing　mode　(TS)　to　reduce　the　crossing-partition　communication.　With　the　change　of　graph　density,　various　factors　such　as　load　balancing,　communication　balancing,　cross-partition　transmission　traffic,　communication　delay,　and　convergence　speed　can　always　maintain　an　efficient　balance.　The　experiments　conducted　on　the　real-world　datasets　show　that　the　communication-equilibrated　graph　partitioning　strategy　can　divide　a　graph　with　high　quality　compared　with　Hash　and　Metis.　Besides,　the　overall　performance　of　our　two-stage　graph　computing　model　with　communication　equilibrium　is　higher　than　that　of　the　BSP　model.　©　2021,　Springer　Nature　Singapore　Pte　Ltd.