ent ▁pla cement ▁with ▁the ▁same ▁edge ▁lengths , ▁but ▁unique ▁realiz ability ▁is ▁stronger ▁than ▁rig id ity . ▁For ▁instance , ▁the ▁diam ond ▁graph ▁( two ▁tri angles ▁sharing ▁an ▁edge ) ▁is ▁rig id ▁in ▁two ▁dimensions , ▁but ▁it ▁is ▁not ▁uniqu ely ▁realiz able ▁because ▁it ▁has ▁two ▁different ▁realiz ations , ▁one ▁in ▁which ▁the ▁tri angles ▁are ▁on ▁opposite ▁sides ▁of ▁the ▁shared ▁edge ▁and ▁one ▁in ▁which ▁they ▁are ▁both ▁on ▁the ▁same ▁side . ▁Un iqu ely ▁realiz able ▁graphs ▁are ▁important ▁in ▁applications ▁that ▁involve ▁reconst ruction ▁of ▁shapes ▁from ▁distances , ▁such ▁as ▁tri ang ulation ▁in ▁land ▁surve ying , ▁the ▁determ ination ▁of ▁the ▁positions ▁of ▁the ▁nodes ▁in ▁a ▁wireless ▁sensor ▁network , ▁and ▁the ▁reconst ruction ▁of ▁conform ations ▁of ▁mole cules ▁via ▁nuclear ▁magnetic ▁reson ance ▁spect ro sc opy . ▁ ▁Bruce ▁Hend rick son ▁defined ▁a ▁graph ▁to ▁be ▁redund antly ▁rig id ▁if ▁it ▁remains ▁rig id ▁after ▁removing ▁any ▁one ▁of ▁its ▁edges . ▁In ▁mat roid al ▁terms , ▁this ▁means ▁that ▁the ▁rig id ity ▁mat roid ▁has ▁the ▁full ▁rank ▁ ▁and ▁that ▁the ▁mat roid ▁does ▁not ▁have ▁any ▁col o ops . ▁Hend rick son ▁proved ▁that ▁every ▁uniqu ely ▁realiz able ▁framework ▁( with ▁generic ▁edge ▁lengths ) ▁is ▁either ▁a ▁complete ▁graph ▁or ▁a ▁- ver tex - connected , ▁redund antly ▁rig id ▁graph , ▁and ▁he ▁conject ured ▁that ▁this ▁is ▁an ▁exact