NFO13018901 Intro Network science14307130355李婧雅 exponent y>3, average shortest length L In(N), cluster coefficient C-N-075 For example, when m,=3, m=2, the procedure of setting up BA scale-free network can be shown FIG 2. The evolutionary of BA scale-free network( mo=3, m=2)[2] 2.3 evolutionary rules 2.3.1 Optimum substitution After every evolutionary, the node compares the payoff of all neighbor nodes and itself and chooses the strategy that the node with highest payoff used as its new game strategy 2.3.2 Fermi rule After every evolutionary, the node i randomly chooses a neighbor node j and according to the difference value between the two decides the possibility of the node i using the node j's strategy in the next game. The possibility can be calculated according to Fermi Function in the statistical physics 1+exp[-(E, -E)/K E, and E represents the payoff the node i and j get in the game When the payoff of i is lower than that of j, i will tend to use j's strategy and the bigger difference value between the two nodes is, the more likely i is to use js strategy. However, when the payoff of i is higher than that of j, it's still possible that i use j's strategy with small possibility. Parameter K represents noise figure which means the behavior can be irrational. It shows the uncertainty in the process of updating strategy. When K>00INFO130189.01 Intro Network Science 14307130355 李婧雅 5 exponent   3, average shortest length L~ ln(N), cluster coefficient C ~ 0.75 N . For example, when m0 =3, m=2, the procedure of setting up BA scale-free network can be shown: FIG 2. The evolutionary of BA scale-free network( m0 =3, m=2)[2] 2.3 evolutionary rules 2.3.1 Optimum substitution After every evolutionary, the node compares the payoff of all neighbor nodes and itself and chooses the strategy that the node with highest payoff used as its new game strategy. 2.3.2 Fermi rule After every evolutionary, the node i randomly chooses a neighbor node j and according to the difference value between the two decides the possibility of the node i using the node j’s strategy in the next game. The possibility can be calculated according to Fermi Function in the statistical physics: 1 exp[ ( ) ] 1 E E K w   i  j  Ei and Ej represents the payoff the node i and j get in the game. When the payoff of i is lower than that of j, i will tend to use j’s strategy and the bigger difference value between the two nodes is, the more likely i is to use j’s strategy. However, when the payoff of i is higher than that of j, it’s still possible that i use j’s strategy with small possibility. Parameter K represents noise figure which means the behavior can be irrational. It shows the uncertainty in the process of updating strategy. When K  