Graph　neural　networks　have　shown　excellent　performance　in　many　fields　owing　to　their　powerful　processing　ability　of　graph　data.　In　recent　years,　federated　graph　neural　network　has　become　a　reasonable　solution　due　to　the　enactment　of　privacy-related　regulations.　However,　frequent　communication　between　the　coordinator　and　participants　in　federated　graph　neural　network　results　in　longer　model　training　time　and　consumes　many　communication　resources.　To　address　this　challenge,　in　this　paper,　we　propose　a　novel　semi-asynchronous　federated　graph　learning　communication　protocol　that　simultaneously　alleviates　the　negative　impact　of　stragglers(slow　participants)　and　accelerate　the　training　process　in　the　unsupervised　federated　graph　neural　network　scenario.　First,　the　weighted　enforced　synchronization　strategy　is　intended　to　preserve　the　information　carried　by　stragglers　while　preventing　their　stale　models　from　harming　the　global　model　update.　Second,　the　adaptive　local　update　strategy　is　developed　to　make　the　local　model　of　the　participant　with　poor　computing　performance　as　close　as　possible　to　the　global　model.　Experiments　combine　federated　learning　with　graph　contrastive　learning.　The　results　demonstrate　that　our　proposed　protocol　outperforms　the　existing　protocols　in　real-world　networks.　©　2024,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.