) ▁Act ▁ 1 7 9 3 ▁ ▁Category : Gre at ▁Britain ▁Act s ▁of ▁Parliament ▁ 1 7 9 3 ▁Category : T reason ▁in ▁the ▁United ▁Kingdom <0x0A> </s> ▁The ▁rich - club ▁coefficient ▁is ▁a ▁metric ▁on ▁graphs ▁and ▁networks , ▁designed ▁to ▁measure ▁the ▁extent ▁to ▁which ▁well - connected ▁nodes ▁also ▁connect ▁to ▁each ▁other . ▁Network s ▁which ▁have ▁a ▁relatively ▁high ▁rich - club ▁coefficient ▁are ▁said ▁to ▁demonstrate ▁the ▁rich - club ▁effect ▁and ▁will ▁have ▁many ▁connections ▁between ▁nodes ▁of ▁high ▁degree . ▁The ▁rich - club ▁coefficient ▁was ▁first ▁introduced ▁in ▁ 2 0 0 4 ▁in ▁a ▁paper ▁studying ▁Internet ▁topology . ▁ ▁This ▁effect ▁has ▁been ▁measured ▁and ▁noted ▁on ▁scientific ▁collaboration ▁networks ▁and ▁air ▁transport ation ▁networks . ▁It ▁has ▁been ▁shown ▁to ▁be ▁significantly ▁lack ing ▁on ▁protein ▁interaction ▁networks . ▁ ▁Definition ▁ ▁Non - normal ized ▁form ▁ ▁The ▁rich - club ▁coefficient ▁was ▁first ▁introduced ▁as ▁an ▁un scale d ▁metric ▁paramet riz ed ▁by ▁node ▁degree ▁ranks . ▁More ▁recently , ▁this ▁has ▁been ▁updated ▁to ▁be ▁parameter ized ▁in ▁terms ▁of ▁node ▁degrees ▁k ▁, ▁indicating ▁a ▁degree ▁cut - off . ▁The ▁rich - club ▁coefficient ▁for ▁a ▁given ▁network ▁N ▁is ▁then ▁defined ▁as : ▁▁▁ ▁where ▁ ▁is ▁the ▁number ▁of ▁edges ▁between ▁the ▁nodes ▁of ▁degree ▁greater ▁than ▁or ▁equal ▁to ▁k , ▁and ▁ ▁is ▁the ▁number ▁of ▁nodes ▁with ▁degree ▁greater ▁than ▁or ▁equal ▁to ▁k .