The　granular　structures　emphasize　a　multilevel　and　multiview　understanding　of　problems.　This　paper　gives　a　study　on　how　to　granulate　a　graph,　and　how　to　extract　the　granular　structures　in　the　graph.　There　are　three　kinds　of　objects　in　the　graph,　vertices,　edges　and　the　combinations　of　vertices　and　edges.　Differing　from　previous　researches　on　graph　clustering　which　focused　on　the　classification　of　vertices,　we　study　three　granular　structure　models　for　the　three　kinds　of　objects　in　the　graph.　©　2012　Springer-Verlag.