Conditional Probability Distribution P(kk)= P(k',k Degree 10 Degree 50 P2(k) Degree 100 Degree 500 Random edge If the network is neutral kP(k) P(k'k)=P(k) oos。8 k 5 5000 Neighbors degree Facebook
( ', ) ( ' | ) ( ) c n P k k P k k P k = ' ( ') ( ' | ) ( ') c n k P k P k k P k k = = If the network is neutral: Facebook
Excess Average Degree Average Next Neighbor degree km)=k6(km)()=∑(m k)(k)=>kP(k|k)=->k If the network is neutral, knn(k)is independent of k: km) 4+3+3+1 aka k')(k k(k) ∑k=∑k <k> R Pastor-Satorras, A Vazquez, A. Vespignani, Phys. Rev. E 65, 066130 (2001
R. Pastor-Satorras, A. Vázquez, A. Vespignani, Phys. Rev. E 65, 066130 (2001) If the network is neutral, knn(k) is independent of k: 2 ' ( ') ( ) k k k nn k k k k k q q k p k k k k k q k q k k = = = = 4 3 3 1 4 nn v k +++ = 1 ( ) ( | ) nn kk k k k k k k P k k k e q = = 1 1 i j k nn i i j i k k k = = 1 1 ( ) k i i nn nn v k i k k k i = =