Graphene　aerogels　(GAs)　are　a　kind　of　advanced　graphene　assemblies,　which　are　quite　elastic　and　can　easily　restore　their　original　form　after　compression.　The　macroscale　compression　behavior　of　the　GAs　is　the　result　of　microstructural　evolution　of　the　graphene　sheets.　In　this　paper,　the　microstructural　compression　response　of　honeycomb-like　GAs　is　investigated　via　coarse-grained　molecular　dynamics　(CGMD)　method.　Based　on　the　coarse-grained　(CG)　model　of　a　single-layer　graphene,　honeycomb-like　structures　can　be　built　and　arranged　layer-by-layer　to　form　the　complete　GA　model.　CGMD　simulations　presented　in　this　work　are　carried　out　with　a　TersoffCG　potential,　which　was　developed　specifically　for　single-layer　graphene.　The　effects　of　layer　number,　size　of　the　graphene　sheets　and　the　interlaminar　overlap　pattern　on　the　compressive　behavior　of　the　GAs　are　studied.　Moreover,　the　stress　distribution　in　graphene　networks　of　the　GAs　during　the　compression　process　is　analyzed.　Different　microscale　strain　concentrations　and　stress　localizations　are　discovered　in　the　GAs　with　different　network　patterns.　Furthermore,　a　negative　Poisson＇s　ratio　of　the　models　within　a　certain　range　of　compressive　strain　is　found,　which　is　related　to　both　the　microstructural　arrangement　and　the　deformation　of　graphene　sheet.　(C)　2018　Elsevier　Ltd.　All　rights　reserved.