Table 1.

Metrics characterizing music albums and their relationships with the tag co-occurrence network.

nameformulamain quantities/notation
topical entropyE(a)=lLaf(l)logf(l)log|La|f(l)=fraction of tags in Ta with label (topic) l
average time spanTS(a)=eEa|ytag2ytag1||Ea|ytag=creation time of the tag tag
average tag ageA(a)=tagTa(yaytag)/(ya1950)|Ta|
mainstreamnessM(a)=12fF212..2=Hellinger distance
burstinessB(a)=lLaf(l)Nl(ya+1)Nl(ya)Nl(ya)Nl(ya)=number of tags with label l until year y
noveltyfnew(a)=|TaT(ya1)||Ta||.∖.|= set difference
adjacent possibleAdj(a)=tagTafAdj(tag,ya)|Ta|fAdj(tag,ya)=fractions of nodes entering in the adjacent possible of tag during ya.
Uchroniauch(a)=1|Ta|tagTauch(tag)(1N(tag,ya)N(tag))uch(tag)=percentage of G destroyed by the removal of tag
N(tag)=number of albums containing tag
N(tag,ya)=number of albums containing tag till year ya
Uchronia entropyhuch(a)=1|Ta|tagTahuch(tag)(1N(tag,ya)N(tag))huch(tag)=variation of the entropy of F after the removal of tag from G.