▁k ▁we ▁have ▁ ▁, ▁this ▁denotes ▁the ▁presence ▁of ▁the ▁rich - club ▁effect . ▁ ▁General izations ▁ ▁General ▁rich ness ▁properties ▁▁ ▁The ▁natural ▁definition ▁of ▁a ▁node ' s ▁" rich ness " ▁is ▁its ▁number ▁of ▁neighb ours . ▁If ▁instead ▁we ▁replace ▁this ▁with ▁a ▁generic ▁rich ness ▁metric ▁on ▁nodes ▁r , ▁then ▁we ▁can ▁rewrite ▁the ▁un scale d ▁Rich - Cl ub ▁coefficient ▁as : ▁ ▁Where ▁we ▁are ▁instead ▁considering ▁the ▁sub ▁graph ▁on ▁only ▁nodes ▁with ▁a ▁rich ness ▁measure ▁of ▁at ▁least ▁r . ▁For ▁example , ▁on ▁scientific ▁collaboration ▁networks , ▁replacing ▁the ▁degree ▁rich ness ▁( number ▁of ▁co auth ors ) ▁with ▁a ▁strength ▁rich ness ▁( number ▁of ▁published ▁papers ), ▁the ▁topology ▁of ▁the ▁rich ▁club ▁graph ▁changes ▁dram atically . ▁ ▁Rel ated ▁metrics ▁ ▁Ass ort ativity ▁▁ ▁The ▁Ass ort ativity ▁of ▁a ▁network ▁is ▁a ▁measurement ▁of ▁how ▁connected ▁similar ▁nodes ▁are , ▁where ▁similarity ▁is ▁typically ▁viewed ▁in ▁terms ▁of ▁node ▁degree . ▁Rich - club ▁can ▁be ▁viewed ▁as ▁a ▁more ▁specific ▁notation ▁of ▁associ ativity , ▁where ▁we ▁are ▁only ▁concerned ▁with ▁the ▁connect ivity ▁of ▁nodes ▁beyond ▁a ▁certain ▁rich ness ▁metric . ▁For ▁example , ▁if ▁a ▁network ▁consisted ▁of ▁a ▁collection ▁of ▁hub ▁and ▁sp okes , ▁where ▁the ▁hub s ▁were ▁well ▁connected , ▁such ▁a ▁network ▁would ▁be ▁considered ▁dis ass ort ative . ▁However , ▁due ▁to ▁the ▁strong ▁connected ness ▁of ▁the