网络社区结构和局部损伤的恢复力：应用于脑微循环
Network community structure and resilience to localized damage: application to brain microcirculation
摘要：
在脑血管网络中，一些顶点彼此之间的连接比与血管系统的其余部分的连接更多，从而定义了社区结构。在这里，我们介绍了一类通过重新布线随机正则图构建的模型网络，它能够重现脑血管网络的这种社区结构和其他拓扑特性。我们使用这些模型网络来研究由去除单个边缘引起的全局流量减少。我们分析表明，这种全球性的流量减少可以表示为在删除的边缘和拓扑量，这两个显示概率分布柯西定律，即大尾巴的初始流量的函数。因此，我们表明，血流减少的分布是强烈的影响，社区结构。特别是，大流量减少的可能性大大增加时，社区结构是较强的，削弱了网络的弹性，单一毛细管闭塞。我们讨论的背景下，阿尔茨海默氏病，其中血管机制，包括毛细血管闭塞的重要性，这些发现的影响，开始被发现。
英文摘要：
In cerebrovascular networks, some vertices are more connected to each other than with the rest of the vasculature, defining a community structure. Here, we introduce a class of model networks built by rewiring Random Regular Graphs, which enables to reproduce this community structure and other topological properties of cerebrovascular networks. We use these model networks to study the global flow reduction induced by the removal of a single edge. We analytically show that this global flow reduction can be expressed as a function of the initial flow rate in the removed edge and of a topological quantity, both of which display probability distributions following Cauchy laws, i.e. with large tails. As a result, we show that the distribution of blood flow reductions is strongly influenced by the community structure. In particular, the probability of large flow reductions increases substantially when the community structure is stronger, weakening the network resilience to single capillary occlusions. We discuss the implications of these findings in the context of Alzheimer's Disease, in which the importance of vascular mechanisms, including capillary occlusions, is beginning to be uncovered.
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