分簇网络中的可观测性变迁
Observability transitions in clustered networks
摘要：
我们研究了聚类对网络可观测性转换的影响。在杨，王，和Motter [物理学评论Lett. 109，258701（2012）]，随机选择给定比例的节点，并且它们和那些邻居被认为是可观察的，而其他节点是不可观察的。对于随机簇网络的可观测性模型，我们导出了最大可观测分量和最大不可观测分量的归一化大小。考虑到每个节点的边和三角形的数量是由泊松分布给出的情况下，我们发现，网络的聚类和LUC都受到影响：更高度聚集的网络具有较低的临界节点分数，以形成宏观的网络和LUC，但这种影响很小，变得几乎可以忽略不计，除非平均度很小。我们还评估了这些临界点的界限，以确认聚类对网络可观测性转换的微弱或可忽略的影响。蒙特卡罗模拟证实了我们的分析处理的准确性。
英文摘要：
We investigate the effect of clustering on network observability transitions. In the observability model introduced by Yang, Wang, and Motter [Phys. Rev. Lett. 109, 258701 (2012)], a given fraction of nodes are chosen randomly, and they and those neighbors are considered to be observable, while the other nodes are unobservable. For the observability model on random clustered networks, we derive the normalized sizes of the largest observable component (LOC) and largest unobservable component (LUC). Considering the case where the numbers of edges and triangles of each node are given by the Poisson distribution, we find that both LOC and LUC are affected by the network's clustering: more highly-clustered networks have lower critical node fractions for forming macroscopic LOC and LUC, but this effect is small, becoming almost negligible unless the average degree is small. We also evaluate bounds for these critical points to confirm clustering's weak or negligible effect on the network observability transition. The accuracy of our analytical treatment is confirmed by Monte Carlo simulations.
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