论文标题
在不相关的网络上的学位订购 -
Degree-Ordered-Percolation on uncorrelated networks
论文作者
论文摘要
我们分析了程度订购的渗滤（DOP）的属性，该模型在该模型中，网络的节点以程度降低的顺序占据。该规则与众所周知的学位协议相反，该协议用于调查在故意攻击下网络的弹性，到目前为止受到了有限的关注。 DOP的兴趣也是由于其与易感感染感染感受的（SIS）模型的息息相关的兴趣，因为DOP的变化与随机Power-power-powerlaw分布式网络的SIS过渡的消失有关，\ sim k^{ - γ} $。通过使用生成函数形式主义，我们研究了DOP模型在$γ$的网络上的行为，并通过数值模拟验证分析结果。我们发现，渗透阈值在大型网络的极限上以$γ\ le 3 $的限制消失，而它的$γ> 3 $是有限的，尽管它的$γ$在3到4之间的$γ$非常小，并且预响应效果很大。我们还得出了DOP过渡的临界特性，特别是指数如何依赖网络的异质性，确定DOP不属于$γ\ le 3 $的随机渗透的普遍性类别。
We analyze the properties of Degree-Ordered Percolation (DOP), a model in which the nodes of a network are occupied in degree-descending order. This rule is the opposite of the much studied degree-ascending protocol, used to investigate resilience of networks under intentional attack, and has received limited attention so far. The interest in DOP is also motivated by its connection with the Susceptible-Infected-Susceptible (SIS) model for epidemic spreading, since a variation of DOP is related to the vanishing of the SIS transition for random power-law degree-distributed networks $P(k) \sim k^{-γ}$. By using the generating function formalism, we investigate the behavior of the DOP model on networks with generic value of $γ$ and we validate the analytical results by means of numerical simulations. We find that the percolation threshold vanishes in the limit of large networks for $γ\le 3$, while it is finite for $γ>3$, although its value for $γ$ between 3 and 4 is exceedingly small and preasymptotic effects are huge. We also derive the critical properties of the DOP transition, in particular how the exponents depend on the heterogeneity of the network, determining that DOP does not belong to the universality class of random percolation for $γ\le 3$.
