ar ▁graph ▁may ▁be ▁drawn ▁without ▁crossing ▁its ▁vertices ▁in ▁arbitrary ▁positions ▁in ▁the ▁plane , ▁where ▁the ▁same ▁vertex ▁pla cement ▁provides ▁a ▁simultane ous ▁embedding . ▁▁ ▁There ▁are ▁two ▁restricted ▁models : ▁simultane ous ▁geometric ▁embedding , ▁where ▁each ▁graph ▁must ▁be ▁drawn ▁plan ar ly ▁with ▁line ▁segments ▁representing ▁its ▁edges ▁rather ▁than ▁more ▁complex ▁curves ▁restrict ing ▁the ▁two ▁given ▁graphs ▁to ▁sub classes ▁of ▁the ▁plan ar ▁graphs ▁and ▁simultane ous ▁embedding ▁with ▁fixed ▁edges , ▁where ▁curves ▁or ▁b ends ▁are ▁allowed ▁in ▁the ▁edges , ▁but ▁any ▁edge ▁in ▁both ▁graphs ▁must ▁be ▁represented ▁by ▁the ▁same ▁curve ▁in ▁both ▁draw ings . ▁In ▁the ▁un rest rict ed ▁model , ▁any ▁two ▁plan ar ▁graphs ▁can ▁have ▁a ▁simultane ous ▁embedding . ▁ ▁Definition ▁Sim ult aneous ▁embedding ▁is ▁a ▁technique ▁in ▁graph ▁drawing ▁and ▁information ▁visual ization ▁for ▁visual izing ▁two ▁or ▁more ▁different ▁graphs ▁on ▁the ▁same ▁or ▁over la pping ▁sets ▁of ▁l abeled ▁vertices , ▁while ▁avoid ing ▁cross ings ▁within ▁both ▁graphs . ▁Cross ings ▁between ▁an ▁edge ▁of ▁one ▁graph ▁and ▁an ▁edge ▁of ▁the ▁other ▁graph ▁are ▁allowed ; ▁it ▁is ▁only ▁cross ings ▁between ▁two ▁edges ▁of ▁the ▁same ▁graph ▁that ▁are ▁dis allowed . ▁ ▁If ▁edges ▁are ▁allowed ▁to ▁be ▁drawn ▁as ▁pol yl ines ▁or ▁curves , ▁then ▁any ▁plan ar ▁graph ▁may ▁be ▁drawn ▁without ▁cross ings ▁with ▁its ▁vertices ▁in ▁arbitrary ▁positions ▁in ▁the ▁plane . ▁Using ▁the ▁same ▁vertex ▁pla