有向网络的距离骨干网
The distance backbone of directed networks
AI总结：
针对原有加权图距离骨干网挖掘方法仅适用于无向图的局限，研究将该代数原理方法拓展至加权有向图，验证9个不同领域有向网络普遍存在大量冗余，为网络稀疏化与鲁棒性度量提供新工具。
摘要：
在加权图中，两个节点之间的最短路径通常是从所有可能连接中选取的间接路径，这会产生结构冗余，而结构冗余在复杂网络的动力学演化中发挥着关键作用。我们此前开发了一种无参数、基于代数原理的方法，用于揭示这类冗余并挖掘加权图的距离骨干网，该方法已被证实在传播动力学、重要路径推断以及网络鲁棒性量化方面具有重要价值。不过，该方法最初是针对无向图提出的。本文中，我们将这一方法拓展至加权有向图，并对来自社会、生物医学以及技术系统的9个网络中的冗余性和鲁棒性展开研究。我们发现，与无向图类似，以（有向）距离骨干网的规模衡量，有向图通常也存在大量冗余。我们的方法为复杂网络的系统化稀疏化及其鲁棒性度量提供了一种新的工具。
英文摘要：
In weighted graphs the shortest path between two nodes is often reached through an indirect path, out of all possible connections, leading to structural redundancies which play key roles in the dynamics and evolution of complex networks. We have previously developed a parameter-free, algebraically-principled methodology to uncover such redundancy and reveal the distance backbone of weighted graphs, which has been shown to be important in transmission dynamics, inference of important paths, and quantifying the robustness of networks. However, the method was developed for undirected graphs. Here we expand this methodology to weighted directed graphs and study the redundancy and robustness found in nine networks ranging from social, biomedical, and technical systems. We found that similarly to undirected graphs, directed graphs in general also contain a large amount of redundancy, as measured by the size of their (directed) distance backbone. Our methodology adds an additional tool to the principled sparsification of complex networks and the measure of their robustness.
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