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第528行： − − === Fitness model === − Another model where the key ingredient is the nature of the vertex has been introduced by Caldarelli et al.<ref>Caldarelli G., A. Capocci, P. De Los Rios, M.A. Muñoz, Physical Review Letters 89, 258702 (2002)</ref> Here a link is created between two vertices <math>i,j</math> with a probability given by a linking function <math>f(\eta_i,\eta_j)</math> of the [[Fitness model (network theory)|fitnesses]] of the vertices involved. − The degree of a vertex i is given by <ref>Servedio V.D.P., G. Caldarelli, P. Buttà, Physical Review E 70, 056126 (2004)</ref> − − :<math>k(\eta_i)=N\int_0^\infty f(\eta_i,\eta_j) \rho(\eta_j) \, d\eta_j </math> − − If <math>k(\eta_i)</math> is an invertible and increasing function of <math>\eta_i</math>, then − the probability distribution <math>P(k)</math> is given by − − :<math>P(k)=\rho(\eta(k)) \cdot \eta'(k)</math> − − As a result, if the fitnesses <math>\eta</math> are distributed as a power law, then also the node degree does. − − Less intuitively with a fast decaying probability distribution as − <math>\rho(\eta)=e^{-\eta}</math> together with a linking function of the kind − − :<math> f(\eta_i,\eta_j)=\Theta(\eta_i+\eta_j-Z)</math> − − with <math>Z</math> a constant and <math>\Theta</math> the Heavyside function, we also obtain − scale-free networks. − − Such model has been successfully applied to describe trade between nations by using GDP as fitness for the various nodes <math>i,j</math> and a linking function of the kind − <ref>Garlaschelli D., M I Loffredo Physical Review Letters 93, 188701 (2004)</ref> − <ref>Cimini G., T. Squartini, D. Garlaschelli and A. Gabrielli, Scientific Reports 5, 15758 (2015)</ref> − − :<math> \frac{\delta \eta_i\eta_j}{1+ \delta \eta_i\eta_j}.</math>
→Fitness model
然而对于<math>m=1</math>，它表现了赢者通吃的机制，因为可以发现几乎<math>99\%</math> 的节点的度仅为1，而某一个节点的度超级大。当<math>m</math>的值增加时，超级富人和穷人之间的差距减小;当<math>m>14</math>时，我们发现了从赢者通吃机制到富人更富机制的转变。
然而对于<math>m=1</math>，它表现了赢者通吃的机制，因为可以发现几乎<math>99\%</math> 的节点的度仅为1，而某一个节点的度超级大。当<math>m</math>的值增加时，超级富人和穷人之间的差距减小;当<math>m>14</math>时，我们发现了从赢者通吃机制到富人更富机制的转变。
=== 适应度模型 ===
=== 适应度模型 ===