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第849行： − + − + − + − After simplifying this model, the degree distribution is <math>P(k) = 2^{-k}. </math><ref name="dorogovtsev-mendes">{{cite book|last1=Dorogovtsev|first1=S N|last2=Mendes|first2=J F F|title=Evolution of Networks: From Biological Nets to the Internet and WWW|date=2003|publisher=Oxford University Press, Inc.|location=New York, NY, USA|isbn=978-0198515906}}</ref>+ − Based on this growing network, an epidemic model is developed following a simple rule: Each time the new node is added and after choosing the old node to link, a decision is made: whether or not this new node will be infected. The master equation for this epidemic model is:+ − where <math>r_t</math> represents the decision to infect (<math>r_t = 1</math>) or not (<math>r_t = 0</math>). Solving this master equation, the following solution is obtained: <math>\tilde{P}_r(k) = \left(\frac r 2 \right)^k. </math><ref name="cotacallapa-hase">{{cite journal|last1=Cotacallapa|first1=M|last2=Hase|first2=M O|title=Epidemics in networks: a master equation approach|journal=Journal of Physics A|date=2016|volume=49|issue=6|page=065001|doi=10.1088/1751-8113/49/6/065001|bibcode=2016JPhA...49f5001C|arxiv=1604.01049}}</ref>+
→主方程法
: <math>p(k,s,t+1) = \frac 1 t p(k-1,s,t) + \left(1 - \frac 1 t \right)p(k,s,t),</math>
: <math>p(k,s,t+1) = \frac 1 t p(k-1,s,t) + \left(1 - \frac 1 t \right)p(k,s,t),</math>
其中 <math>p(k,s,t)</math> 是 <math>t+1</math>时刻节点<math>s</math>的度为<math>k</math>的概率，<math>s</math>是这个时间步长内新添加到网络中的节点。is the probability to have the node <math>s</math> with degree <math>k</math> at time <math>t+1</math>, and <math>s</math> is the time step when this node was added to the network. Note that there are only two ways for an old node <math>s</math> to have <math>k</math> links at time <math>t+1</math>:
其中 <math>p(k,s,t)</math> 是 <math>t</math>时刻节点<math>s</math>的度为<math>k</math>的概率，<math>s</math>是该节点添加到网络中的时间。为了使老节点<math>s</math>在<math>t+1</math>的度为<math>k</math>，只有两种方法：
* The node <math>s</math> have degree <math>k-1</math> at time <math>t</math> and will be linked by the new node with probability <math>1/t</math>
* 节点<math>s</math> 在<math>t</math>的度为<math>k-1</math>且增加新的边，其概率概率为<math>1/t</math>
* Already has degree <math>k</math> at time <math>t</math> and will not be linked by the new node.
* 节点<math>s</math> 在<math>t</math>的度已经为<math>k</math>，并且没有添加新的边
通过简化模型，可以得到度分布为 <math>P(k) = 2^{-k}. </math><ref name="dorogovtsev-mendes">{{cite book|last1=Dorogovtsev|first1=S N|last2=Mendes|first2=J F F|title=Evolution of Networks: From Biological Nets to the Internet and WWW|date=2003|publisher=Oxford University Press, Inc.|location=New York, NY, USA|isbn=978-0198515906}}</ref>
基于上述生长网络，可以按照以下规则生成流行性模型：每次新添节点并且选择它所连接的老节点时，需要做以下决定：这个新节点是否为感染者。流行病模型的主方程形式为：
: <math>p_r(k,s,t) = r_t \frac 1 t p_r(k-1,s,t) + \left(1 - \frac 1 t \right) p_r(k,s,t),</math>
: <math>p_r(k,s,t) = r_t \frac 1 t p_r(k-1,s,t) + \left(1 - \frac 1 t \right) p_r(k,s,t),</math>
其中 <math>r_t</math> 代表感染者 (<math>r_t = 1</math>) 或者非感染者 (<math>r_t = 0</math>)。求解这个主方程，可以得到这样的解： <math>\tilde{P}_r(k) = \left(\frac r 2 \right)^k. </math><ref name="cotacallapa-hase">{{cite journal|last1=Cotacallapa|first1=M|last2=Hase|first2=M O|title=Epidemics in networks: a master equation approach|journal=Journal of Physics A|date=2016|volume=49|issue=6|page=065001|doi=10.1088/1751-8113/49/6/065001|bibcode=2016JPhA...49f5001C|arxiv=1604.01049}}</ref>
==Interdependent networks==
==Interdependent networks==