Random graph go038(300 When p= 2pc, Connected graph But, generate 10000 G0.039(300) graphs, 2% graphs are disconnected When p=3pc generate 10000 G0.057(300) graphs, Isolated node 100% graphs are Node with degree≤9 connected Node with degree >9
Random Graph G0.038(300) Isolated node Node with degree ≤ 9 Node with degree > 9 When p= 2pc , Connected graph! But, generate 10000 G0.038(300) graphs, 2% graphs are disconnected. When p=3pc , generate 10000 G0.057(300) graphs, 100% graphs are connected
O&A (b )p=3*0.019=0.057, the graphs can be expressed as go.o5z 300) Binomial distribution N 29 P(k)=k p(1-p) 00570943 P(k=299)=0057≈0 When,<k>=(N-1)p=299×0.057=17 We can get the maximum P(kro 17=0.099 (c) The average link number: ElL NN-1 N(N-1vrlogN 2D= ==(N-1)logN≈2558 N 2
(b) p=3*0.019=0.057，the graphs can be expressed as G0.057(300) Binomial distribution (c) The average link number: 1 299 299 1 299 P( ) (1 ) 0.057 0.943 P( 299) 0.057 0 k N k k k rg N k p p k k k ( 1) ( 1) log 3 [ ] 3 ( 1)log 2558 2 2 2 N N N N N E L p N N N Q&A when, We can get the maximum P(krg=17)=0.099. k N p ( 1) 299 0.057 17