1 ▁- ▁C ) ▁if ▁one ▁cons iders ▁C ▁as ▁the ▁cum ulative ▁degree ▁distribution ; ▁ ▁i . e . ▁the ▁complement ▁of ▁C . ▁ ▁Ob ser ved ▁degree ▁distributions ▁ ▁The ▁degree ▁distribution ▁is ▁very ▁important ▁in ▁studying ▁both ▁real ▁networks , ▁such ▁as ▁the ▁Internet ▁and ▁social ▁networks , ▁and ▁theoretical ▁networks . ▁ ▁The ▁simplest ▁network ▁model , ▁for ▁example , ▁the ▁( Er d ős – R ény i ▁model ) ▁random ▁graph , ▁in ▁which ▁each ▁of ▁n ▁nodes ▁is ▁independently ▁connected ▁( or ▁not ) ▁with ▁probability ▁p ▁( or ▁ 1 ▁− ▁p ), ▁has ▁a ▁bin omial ▁distribution ▁of ▁degrees ▁k : ▁ ▁( or ▁Po isson ▁in ▁the ▁limit ▁of ▁large ▁n , ▁if ▁the ▁average ▁degree ▁ ▁is ▁held ▁fixed ). ▁Most ▁networks ▁in ▁the ▁real ▁world , ▁however , ▁have ▁degree ▁distributions ▁very ▁different ▁from ▁this . ▁Most ▁are ▁highly ▁right - ske wed , ▁meaning ▁that ▁a ▁large ▁majority ▁of ▁nodes ▁have ▁low ▁degree ▁but ▁a ▁small ▁number , ▁known ▁as ▁" h ubs ", ▁have ▁high ▁degree . ▁Some ▁networks , ▁not ably ▁the ▁Internet , ▁the ▁world ▁wide ▁web , ▁and ▁some ▁social ▁networks ▁were ▁argued ▁to ▁have ▁degree ▁distributions ▁that ▁approximately ▁follow ▁a ▁power ▁law : ▁, ▁where ▁ γ ▁is ▁a ▁constant . ▁Such ▁networks ▁are ▁called ▁scale - free ▁networks ▁and ▁have ▁attract ed ▁particular ▁attention ▁for ▁their ▁struct ural ▁and ▁dynam ical ▁properties . ▁However , ▁recently , ▁there ▁have ▁been ▁some ▁research