通过强化节点提升空间网络的鲁棒性
Improving robustness of spatial networks via reinforced nodes
AI总结：
本研究通过空间网络模型发现强化节点能显著提升网络鲁棒性，最佳分布策略依赖于渗流阶段，且强化节点在相变中类似外场，满足Widom关系。
摘要：
许多真实世界的网络嵌入在空间中，而它们在存在强化节点时的韧性尚未被研究。在此，我们使用一种空间网络模型来模拟此类网络，该模型的链接长度 $r$ 呈指数分布，具有特征长度 $ζ$。我们发现强化节点能显著提高网络的韧性，且这种提升随空间嵌入的强度而变化。我们还研究了不同的强化节点分布策略以提升网络韧性。有趣的是，我们发现最佳策略高度依赖于渗流过程的阶段，即预期的故障比例。最后，我们表明强化节点在渗流相变中类似于外场，即具有相同的临界指数，且这些临界指数满足 Widom 关系。
英文摘要：
Many real-world networks are embedded in space, and their resilience in the presence of reinforced nodes has not been studied. Here we model such networks using a spatial network model that have an exponential distribution of link length $r$ having a characteristic length $ζ$. We find that reinforced nodes can significantly increase the resilience of the networks which varies with strength of spatial embedding. We also study different reinforced node distribution strategies for improving the network resilience. Interestingly, we find that the best strategy is highly dependent on the stage of the percolation process, i.e., the expected fraction of failures. Finally, we show that the reinforced nodes are analogous to an external field in percolation phase transition i.e., having the same critical exponents and that the critical exponents satisfy Widom's relation.
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