复杂网络中路径的层次性
Routes Obey Hierarchy in Complex Networks
摘要：
关于复杂网络中节点之间的通信路径，存在着各种各样的假设。大多数研究只是假设通信通过最短路径进行，而其他研究则对路由（或者导航或搜索）在真实网络中如何工作或应该如何工作有更明确的假设。然而，这些假设很少与实际数据进行核对。在这里，我们直接分析使用实际测量的操作路径的结构。为此，我们使用现有的和新创建的数据集，这些数据集既具有网络拓扑结构，又具有足够数量的经验确定的路径。这些数据集针对航空运输网络、人脑、互联网和fit-fat-cat进行处理。词梯游戏。我们的研究结果表明，从大量的可能路径，自然似乎选择根据一些简单的规则，我们将称为路由策略。首先，我们确认，短路径的偏好是一个不可避免的政策因素，然而，观察到的路径的延伸表明，有其他政策同时在工作。我们确定了两个额外的政策共同在我们的网络：“符合层次结构”，这意味着路径应该服从网络的结构层次结构，和“首选下游”的政策，促进避免网络核心，如果可能的话。基于这些简单的政策，我们提出了一个合成的路由策略，可以恢复网络中的操作路径的基本统计特性。我们的结果可以帮助估计反应的复杂系统的应力来自外部更准确地比最短路径假设允许。
英文摘要：
Various hypotheses exist about the paths used for communication between the nodes of complex networks. Most studies simply suppose that communication goes via shortest paths, while others have more explicit assumptions about how routing (alternatively navigation or search) works or should work in real networks. However, these assumptions are rarely checked against real data. Here we directly analyze the structure of operational paths using real measurements. For this purpose we use existing and newly created datasets having both the topology of the network and a sufficient number of empirically-determined paths over it. Such datasets are processed for air transportation networks, the human brain, the Internet and the fit-fat-cat word ladder game. Our results suggest that from the great number of possible paths, nature seems to pick according to some simple rules, which we will refer to as routing policies. First we confirm, that the preference of short paths is an inevitable policy element, however the observed stretch of the paths suggests that there are other policies at work simultaneously. We identify two additional policies common in our networks: the "conform hierarchy", meaning that the paths should obey the structural hierarchy of the network, and the "prefer downstream" policy which promotes avoiding the network core if possible. Building upon these simple policies, we propose a synthetic routing policy which can recover the basic statistical properties of the operational paths in networks. Our results can be helpful in estimating the reaction of complex systems for stress coming from the outside more accurately than the shortest path assumption permits.
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