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| | 注意，平均路径长度随N的变化和半径相同。 | | 注意，平均路径长度随N的变化和半径相同。 |
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| − | ====Mediation-driven attachment (MDA) model==== | + | ====中介驱动依附(MDA)模型==== |
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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
| + | 在[[中介驱动依附模型|中介驱动依附(MDA)模型]]中，一个带有<math>m</math>边的新节点随机选择一个已连接的节点，然后不与那个节点连接，而是随机地与它的<math>m</math>个邻居连接。随机选择已连接节点的概率<math>\Pi(i)</math> 为 |
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| | : <math> \Pi(i) = \frac{k_i} N \frac{ \sum_{j=1}^{k_i} \frac 1 {k_j} }{k_i}.</math> | | : <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
| + | 向量 <math>\frac{\sum_{j=1}^{k_i}{\frac{1}{k_j}}}{k_i}</math>是节点 <math>i</math>的<math>k_i</math>个相邻节点的度的调和平均（IHM）的逆。大量的数值研究表明，对于<math>m> 14</math>，IHM的值在大<math>N</math>极限下会变成常数，这意味着<math>\Pi(i) \propto k_i</math>。这表明一个节点的度越高，他就有更大的机会获得更多的连接，因为它们可以通过中介以更多的方式达到，这本质上体现了富人越富机制的直观思想（或者BA模型优先链接的规则）。因此，可以看出MDA网络遵循优先链接规则，但是是伪装的。<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> |
| − | (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.
| + | 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。 |
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| | === Fitness model === | | === Fitness model === |