论文标题
在最佳供应网络中的不连续过渡到循环形成
Discontinuous transition to loop formation in optimal supply networks
论文作者
论文摘要
最佳供应网络的结构和设计是复杂网络研究中的重要主题。自然和人造网络的基本特征是循环的出现和构成的权衡：在供应网络中增加冗余边缘是昂贵的，但对弹性有益。循环通常会形成新边缘成本小或输入不确定时。在这里，我们进一步阐明了向循环形成的过渡。我们证明，当降低边缘损伤模型和波动的水槽模型的新边缘成本时，环路出现了。从数学上讲，新回路通过马鞍节分叉形成。我们的分析允许启发性地预测第一个循环出现的位置和成本。最后，我们在中间度量与最佳树网络之间建立了亲密关系。我们的结果可用于了解现实世界生物网络中循环形成的演变。
The structure and design of optimal supply networks is an important topic in complex networks research. A fundamental trait of natural and man-made networks is the emergence of loops and the trade-off governing their formation: adding redundant edges to supply networks is costly, yet beneficial for resilience. Loops typically form when costs for new edges are small or inputs uncertain. Here, we shed further light on the transition to loop formation. We demonstrate that loops emerge discontinuously when decreasing the costs for new edges for both an edge-damage model and a fluctuating sink model. Mathematically, new loops are shown to form through a saddle-node bifurcation. Our analysis allows to heuristically predict the location and cost where the first loop emerges. Finally, we unveil an intimate relationship among betweenness measures and optimal tree networks. Our results can be used to understand the evolution of loop formation in real-world biological networks.
