Blockchain　allows　for　secure　management　of　a　shared　ledger　by　agreement　protocols,　where　transactions　are　validated　over　network　without　central　authorities.　Although　the　agreement　protocol　has　been　thoroughly　conducted　of　propagation　and　consensus　researches,　mobility　of　nodes　in　unstructured　overlay　networks　has　not　received　much　attention.　Besides,　current　dynamic　propagation　schemes　waste　travel　hops　and　are　low　of　delivery　ratio.　In　this　article,　we　propose　a　social　characteristic-based　propagation-efficient　protocol　NefSBFT　to　agree　on　system　state　plus　consensus　mechanisms　in　public　blockchains.　We　devise　a　propagation　technique　(travel　hops　of　at　least1/3　savings,　delivery　ratio　above　0.93,　etc.)　for　message　multicasting　when　exploiting　real　nodes＇　social　characteristics　of　intermittent　connectivity　and　frequent　partitions.　This　propagation　technique　is　executed　in　the　improved　FastBFT　to　achieve　transaction　ordering　and　block　verification,　thus,　no　controllable　mobility　is　required　during　the　whole　system＇s　execution.　NefSBFT　achieves　fast　propagation,　small　message　complexity　and　few　resource　consumption　of　travel　hops　and　running　nodes　for　complete　protocol　execution.　We　analyze　NefSBFT＇s　security　against　DDOS　attack　of　non-primary　failure.　The　experiments　show　the　performance　tradeoff　under　different　parameters,　compare　the　propagation　efficiency　with　Erlay　and　Flooding,　and　clarify　NefSBFT＇s　impact　on　the　whole　system　performance　through　comparison.