Recommendations　are　important　web　services　in　the　era　of　information　explosion.　Particularly,　group　recommendations　aim　to　suggest　new　items　to　groups　such　that　the　members　of　groups　are　likely　interested　in.　However,　existing　works　still　suffer　from　sparsity　and　cold-start　issues　(e.g.,　cold-start　groups　or　items)　for　groups　with　few　interactions　on　items.　Most　of　them　model　the　preferences　or　features　of　entities　(i.e.,　users,　items　and　groups)　from　heterogeneous　interactions　(i.e.,　user-item,　group-item　and　user-group　interactions)　between　two　distinct　types　of　entities,　while　ignoring　the　homogeneous　interactions　(i.e.,　user-user,　item-item　and　group-group　interactions)　between　entities　of　one　type.　To　this　end,　we　propose　a　new　model,　called　H3Rec,　which　learns　the　representations　of　entities　by　developing　two　graph　embedding　layers　based　on　an　interaction　graph　of　all　entities.　Specifically,　the　two　graph　embedding　layers　make　full　use　of　the　hidden　information　in　the　Higher-order　Heterogeneous　and　Homogeneous　interactions　of　the　graph.　Therefore,　H3Rec　can　alleviate　the　sparsity　and　cold-start　issues　and　improve　the　performance　of　group　recommendations.　The　experimental　results　on　two　real　world　datasets　in　different　domains　show　the　superiority　of　H3Rec　in　group　recommendations,　especially　for　cold-start　groups　and　items.　IEEE