12 −3 −2 −1 0 1 −4 −3 −2 −1 0 R $^{2}$= 0.93581 (a) log$_{10}$[( ℓ − ℓ$_{1}$ ) /z ] −4 −3 −2 −1 0 −3 −2 −1 0 R $^{2}$= 0.93446 (b) log$_{10}$[( ℓ − ℓ$_{1}$ ) / ( ℓz )] −4 −3 −2 −1 0 −3 −2 −1 0 R $^{2}$= 0.92422 (c) log$_{10}$[( ℓ − ℓ$_{1}$ ) / ( ℓ$_{1}$z )] −2 −1 0 1 −4 −3 −2 −1 0 R $^{2}$= 0.76719 (d) log$_{10}$( ℓ/z ) −2 −1 0 1 2 −4 −3 −2 −1 0 R $^{2}$= 0.76833 (e) log$_{10}$( ℓ − ℓ$_{1}$ ) 0 0.5 1 1.5 2 −4 −3 −2 −1 0 R $^{2}$= 0.71128 (f) log$_{10}$( ℓ ) −2 −1 0 1 −4 −3 −2 −1 0 R $^{2}$= 0.54382 (g) log$_{10}$( ℓ$_{1}$/z ) −2.5 −2 −1.5 −1 −0.5 0 −4 −3 −2 −1 0 R $^{2}$= 0.56967 (h) log$_{10}$(1 /z ) −2 −1 0 1 −4 −3 −2 −1 0 R $^{2}$= 0.60585 (i) log$_{10}$[( ℓ − ℓ$_{1}$ ) /ℓ$_{1}$ ] 0.2 0.4 0.6 0.8 1 1.2 −4 −3 −2 −1 0 R $^{2}$= 0.37255 (j) log$_{10}$( ℓ$_{1}$ ) 0 0.5 1 1.5 −4 −3 −2 −1 0 R $^{2}$= 0.36790 Power Grid PGP Network AS Internet RL Internet Coauthorships Airports500 Interacting Proteins C. Elegans Metabolic C. Elegans Neural Facebook Caltech Facebook Georgetown Facebook Oklahoma Facebook UNC WS:  z =10,  N =1000 WS:  z =10,  N =10000 (3,3)=1,  N =1002 (3,3)=1,  N =10002 (k) log$_{10}$( ℓ/ℓ$_{1}$ ) −3 −2.5 −2 −1.5 −1 −0.5 −4 −3 −2 −1 0 R $^{2}$= 0.80406 (l) log$_{10}$( ˜ C/z ) −3 −2.5 −2 −1.5 −1 −0.5 −4 −3 −2 −1 0 R $^{2}$= 0.01251 (m) log$_{10}$( ˜ C/ℓ ) −2.5 −2 −1.5 −1 −0.5 0 −4 −3 −2 −1 0 R $^{2}$= 0.20134 (n) log$_{10}$( ˜ C ) −2 −1.5 −1 −0.5 0 −4 −3 −2 −1 0 R $^{2}$= 0.08680 (o) log$_{10}$( C ) log 10 E