There　are　plenty　of　researches　on　group　decision　making　(GDM)　problem　and　most　of　them　assume　that　all　the　experts　are　independent.　However,　the　social　network　connection　is　an　important　characteristic　among　experts,　and　should　been　taken　into　account　in　the　GDM　decision　process.　The　social　network　analysis　(SNA)　is　a　rapidly　developing　technology　to　deal　with　the　problem　about　social　network　connections.　In　this　paper,　we　address　GDM　problem　with　fuzzy　preference　relations　where　the　experts　have　directed　social　network　connections.　And　we　use　in-degree　and　out-degree　centrality　indices　in　SNA　to　build　the　social　characteristics　of　the　experts.　Then　we　utilize　the　importance　induced　ordered　weighted　averaging　(I-IOWA)　operator　to　aggregate　all　the　individual　fuzzy　preference　relations　with　social　indices.　Furthermore,we　investigate　the　reciprocity,　additive　consistency　and　acceptable　consistency　properties　about　the　obtained　group　fuzzy　preference　relations.　A　procedure　of　addressing　GDM　problem　with　fuzzy　preference　relations　where　the　experts　are　within　directed　social　network　connections　is　developed.　Moreover,　we　compare　the　results　of　the　case　where　all　the　experts　are　independent　and　the　case　where　all　the　experts　are　within　directed　social　network　connections.　Some　useful　tips　that　affect　final　outranking　result　in　the　directed　graphical　social　network　connection　are　obtained.　In　the　end,　we　summarize　the　main　results　of　this　paper　and　point　out　some　research　directions　for　future　research.