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第194行： − We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong local clustering around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is small world, that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.+ 第202行：
第202行： − Also we can compute the final number of people who once spread the news, this is given by − r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty} − In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of r_\infty as a function of the rewiring probability p. − + + + +
→= = 社会网络中的传染病模型 = =
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意，如果我们在一个节点周围有一个强大的本地集群，那么可能发生的情况是，许多节点成为传播者，并且有作为传播者的邻居。然后，每次我们选择其中之一，他们将恢复，并可以消除谣言传播。另一方面，如果我们有一个世界很小的网络，也就是说，在一个网络中，两个随机选择的节点之间的最短路径比预期的要小得多，我们可以预期谣言会传播得很远。
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意，如果我们在一个节点周围有一个强大的本地集群，那么可能发生的情况是，许多节点成为传播者，并且有作为传播者的邻居。然后，每次我们选择其中之一，他们将恢复，并可以消除谣言传播。另一方面，如果我们有一个世界很小的网络，也就是说，在一个网络中，两个随机选择的节点之间的最短路径比预期的要小得多，我们可以预期谣言会传播得很远。
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.
我们还可以计算最终传播消息的人数，这是由 r _ infty = 1-e ^ {-({ alpha + beta over beta }) r _ infty 给出的。在网络中，在一个完全混合的人口中没有一个阈值的过程，在小世界中表现出明显的相变。下图说明了 r _ infty 的渐近值作为重新布线概率 p 的函数。
我们还可以计算最终传播消息的人数，这是由<br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br />
给出的。在网络中，在一个完全混合的人口中没有一个阈值的过程，在小世界中表现出明显的相变。下图说明了 r _ infty 的渐近值作为重新布线概率 p 的函数。
=== Microscopic models ===
=== Microscopic models ===