▁the ▁fragment ▁ ions ▁in ▁the ▁experimental ▁spectrum ▁are ▁found , ▁they ▁are ▁extended ▁by ▁resid ues ▁one ▁by ▁one ▁to ▁find ▁the ▁best ▁matching . ▁ ▁In ▁the ▁third ▁method , ▁graph ical ▁display ▁of ▁the ▁data ▁is ▁applied , ▁in ▁which ▁fragment ▁ ions ▁that ▁have ▁the ▁same ▁mass ▁differences ▁of ▁one ▁am ino ▁acid ▁resid ue ▁are ▁connected ▁by ▁lines . ▁In ▁this ▁way , ▁it ▁is ▁easier ▁to ▁get ▁a ▁clear ▁image ▁of ▁ion ▁series ▁of ▁the ▁same ▁type . ▁This ▁method ▁could ▁be ▁helpful ▁for ▁manual ▁de ▁nov o ▁pe pt ide ▁sequ encing , ▁but ▁doesn ’ t ▁work ▁for ▁high - through put ▁condition . ▁ ▁The ▁fourth ▁method , ▁which ▁is ▁considered ▁to ▁be ▁successful , ▁is ▁the ▁graph ▁theory . ▁App lying ▁graph ▁theory ▁in ▁de ▁nov o ▁pe pt ide ▁sequ encing ▁was ▁first ▁mentioned ▁by ▁Bart els . ▁Pe aks ▁in ▁the ▁spectrum ▁are ▁transformed ▁into ▁vertices ▁in ▁a ▁graph ▁called ▁“ spect rum ▁graph ”. ▁If ▁two ▁vertices ▁have ▁the ▁same ▁mass ▁difference ▁of ▁one ▁or ▁several ▁am ino ▁ac ids , ▁a ▁directed ▁edge ▁will ▁be ▁applied . ▁The ▁Seq MS ▁algorithm , ▁L ute f isk ▁algorithm , ▁Sher eng a ▁algorithm ▁are ▁some ▁examples ▁of ▁this ▁type . ▁ ▁Software ▁packages ▁As ▁described ▁by ▁Andre otti ▁et ▁al ▁ ▁in ▁ 2 0 1 2 , ▁An til ope ▁is ▁a ▁combination ▁of ▁L agr ang ian ▁relax ation ▁and ▁an ▁adaptation ▁of ▁Y en ' s ▁k