复杂网络中模型过度简化导致的中心性异常
Centrality anomalies in complex networks as a result of model over-simplification
摘要：
我们对复杂网络的性质和演化的理解已经取得了巨大的进步。这些进展最初是由信息贫乏的经验网络和对无权无向图的理论分析推动的。最近，信息丰富的经验数据复杂网络支持更复杂的模型，包括边缘方向性和权重属性，以及多个层的发展。许多研究仍然集中在网络的无向描述，这就引出了一个基本问题：如何识别一个模型是否比它必须的更简单？在这里，我们认为，复杂网络中的中心性异常的存在是模型过度简化的结果。具体来说，我们研究了交通网络介数中心性的众所周知的异常，根据该异常，高度连接的节点不一定是最中心的。使用广泛的一类网络模型的权重和空间约束和四个大型数据集的交通网络，我们表明，这些网络的结构的未加权投影可以表现出显着比例的异常节点相比，随机零模型。然而，这些网络的加权投影，与适当的空模型相比，显着降低了观察到的异常的比例，表明中心性异常是模型过度简化的症状。由于缺乏信息丰富的数据是处理复杂网络时的一个常见挑战，并可能导致错误估计系统中节点的作用的异常，我们认为，当检测到异常时，应使用足够复杂的模型。
英文摘要：
Tremendous advances have been made in our understanding of the properties and evolution of complex networks. These advances were initially driven by information-poor empirical networks and theoretical analysis of unweighted and undirected graphs. Recently, information-rich empirical data complex networks supported the development of more sophisticated models that include edge directionality and weight properties, and multiple layers. Many studies still focus on unweighted undirected description of networks, prompting an essential question: how to identify when a model is simpler than it must be? Here, we argue that the presence of centrality anomalies in complex networks is a result of model over-simplification. Specifically, we investigate the well-known anomaly in betweenness centrality for transportation networks, according to which highly connected nodes are not necessarily the most central. Using a broad class of network models with weights and spatial constraints and four large data sets of transportation networks, we show that the unweighted projection of the structure of these networks can exhibit a significant fraction of anomalous nodes compared to a random null model. However, the weighted projection of these networks, compared with an appropriated null model, significantly reduces the fraction of anomalies observed, suggesting that centrality anomalies are a symptom of model over-simplification. Because lack of information-rich data is a common challenge when dealing with complex networks and can cause anomalies that misestimate the role of nodes in the system, we argue that sufficiently sophisticated models be used when anomalies are detected.
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