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| | 由于Watts–Strogatz 模型的初始网络具有非随机的规则结构，它具有很高的聚集系数和平均路径长度。每次重新连接都可能在高度连接的集群之间创建一条捷径。随着重连接概率的增加，聚集系数的下降速度慢于平均路径长度。实际上，这使得网络的平均路径长度显著降低，而聚集系数只略微降低。更高的重连接概率<math>p</math>会导致更多的边重新连接，这实际上使Watts Strogatz模型趋于随机网络。 | | 由于Watts–Strogatz 模型的初始网络具有非随机的规则结构，它具有很高的聚集系数和平均路径长度。每次重新连接都可能在高度连接的集群之间创建一条捷径。随着重连接概率的增加，聚集系数的下降速度慢于平均路径长度。实际上，这使得网络的平均路径长度显著降低，而聚集系数只略微降低。更高的重连接概率<math>p</math>会导致更多的边重新连接，这实际上使Watts Strogatz模型趋于随机网络。 |
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| − | ====Mediation-driven attachment (MDA) model====
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| − | In the [[mediation-driven attachment model|mediation-driven attachment (MDA) model]] in which a new node coming with <math>m</math> edges picks an existing connected node at random and then connects itself not with that one but with <math>m</math> of its neighbors chosen also at random. The probability <math>\Pi(i)</math> that the node <math>i</math> of the existing node picked is
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| − | : <math> \Pi(i) = \frac{k_i} N \frac{ \sum_{j=1}^{k_i} \frac 1 {k_j} }{k_i}.</math>
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| − | The factor <math>\frac{\sum_{j=1}^{k_i}{\frac{1}{k_j}}}{k_i}</math> is the inverse of the harmonic mean
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| − | (IHM) of degrees of the <math>k_i</math> neighbors of a node <math>i</math>. Extensive numerical investigation suggest that for an approximately <math>m> 14</math> the mean IHM value in the large <math>N</math> limit becomes a constant which means <math>\Pi(i) \propto k_i</math>. It implies that the higher the
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| − | links (degree) a node has, the higher its chance of gaining more links since they can be
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| − | reached in a larger number of ways through mediators which essentially embodies the intuitive
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| − | idea of rich get richer mechanism (or the preferential attachment rule of the Barabasi–Albert model). Therefore, the MDA network can be seen to follow
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| − | the PA rule but in disguise.<ref>{{cite journal | last1 = Hassan | first1 = M. K. | last2 = Islam | first2 = Liana | last3 = Arefinul Haque | first3 = Syed | date = March 2017 | title = Degree distribution, rank-size distribution, and leadership persistence in mediation-driven attachment networks | doi = 10.1016/j.physa.2016.11.001 | journal = Physica A | volume = 469 | issue = | pages = 23–30 | arxiv = 1411.3444 | bibcode = 2017PhyA..469...23H }}</ref>
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| − | However, for <math>m=1</math> it describes the winner takes it all mechanism as we find that almost <math>99\%</math> of the total nodes have degree one and one is super-rich in degree. As <math>m</math> value increases the disparity between the super rich and poor decreases and as <math>m>14</math> we find a transition from rich get super richer to rich get richer mechanism.
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| | === Barabási–Albert (BA) 优先链接模型 === | | === Barabási–Albert (BA) 优先链接模型 === |