. ▁Ind ividual ▁in - ne igh b ors ▁are ▁denoted ▁as ▁, ▁for ▁, ▁and ▁individual ▁out - ne igh b ors ▁are ▁denoted ▁as ▁, ▁for ▁. ▁ ▁Let ▁us ▁denote ▁the ▁similarity ▁between ▁objects ▁ ▁and ▁ ▁by ▁. ▁ ▁Following ▁the ▁earlier ▁motiv ation , ▁a ▁recursive ▁equation ▁is ▁written ▁for ▁. ▁If ▁ ▁then ▁ ▁is ▁defined ▁to ▁be ▁. ▁Otherwise , ▁ ▁where ▁ ▁is ▁a ▁constant ▁between ▁ ▁and ▁. ▁A ▁slight ▁technical ity ▁here ▁is ▁that ▁either ▁ ▁or ▁ ▁may ▁not ▁have ▁any ▁in - ne igh b ors . ▁Since ▁there ▁is ▁no ▁way ▁to ▁infer ▁any ▁similarity ▁between ▁ ▁and ▁ ▁in ▁this ▁case , ▁similarity ▁is ▁set ▁to ▁, ▁so ▁the ▁summ ation ▁in ▁the ▁above ▁equation ▁is ▁defined ▁to ▁be ▁ ▁when ▁ ▁or ▁. ▁ ▁Matrix ▁representation ▁of ▁Sim R ank ▁▁ ▁Let ▁ ▁be ▁the ▁similarity ▁matrix ▁whose ▁entry ▁ ▁denotes ▁the ▁similarity ▁score ▁, ▁and ▁ ▁be ▁the ▁column ▁normal ized ▁adj ac ency ▁matrix ▁whose ▁entry ▁ ▁if ▁there ▁is ▁an ▁edge ▁from ▁ ▁to ▁, ▁and ▁ 0 ▁otherwise . ▁Then , ▁in ▁matrix ▁not ations , ▁Sim R ank ▁can ▁be ▁form ulated ▁as ▁ ▁where ▁ ▁is ▁an ▁identity ▁matrix . ▁ ▁Comput ing ▁Sim R ank ▁▁ ▁A ▁solution ▁to ▁the ▁Sim R ank ▁equations ▁for ▁a ▁graph ▁ ▁can ▁be ▁reached ▁by ▁iteration ▁to ▁a ▁fixed - point . ▁Let ▁ ▁be ▁the ▁number ▁of ▁nodes ▁in ▁. ▁For ▁each ▁iteration