School of Mathematics, University of Birmingham, Birmingham B15 2TT, United Kingdom.
Topological Design Centre for Doctoral Training, University of Birmingham, Birmingham B15 2TT, United Kingdom.
Proc Natl Acad Sci U S A. 2023 Mar 21;120(12):e2215752120. doi: 10.1073/pnas.2215752120. Epub 2023 Mar 16.
In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean degree and degree-degree correlations. And it has important implications for other properties of real networks and the dynamical behavior of many complex systems. We find that strong connectivity depends crucially on the extent to which the network has an overall direction or hierarchical ordering-a property measured by trophic coherence. Using percolation theory, we find the critical point separating weakly and strongly connected regimes and confirm our results on many real-world networks, including ecological, neural, trade, and social networks. We show that the connectivity structure can be disrupted with minimal effort by a targeted attack on edges which run counter to the overall direction. This means that many dynamical processes on networks can depend significantly on a small fraction of edges.
在许多真实的有向网络中，相互可达节点的强连通分量非常小。这与当前基于随机图的理论不符，根据该理论，强连通性取决于平均度数和度-度相关性。这对真实网络的其他性质和许多复杂系统的动力学行为都有重要影响。我们发现，强连通性取决于网络整体方向或层次排序的程度——这一性质可以通过营养一致性来衡量。我们利用渗流理论找到了区分弱连通和强连通区域的临界点，并在包括生态、神经、贸易和社交网络在内的许多真实网络上验证了我们的结果。我们表明，通过针对与整体方向相反的边进行有针对性的攻击，可以以最小的代价破坏连通结构。这意味着网络上的许多动力学过程可能很大程度上取决于一小部分边。
