The extraction of a clear and simple footprint of the structure of large, weighted and directed networks is a general problem that has relevance for many applications. An important example is seen in origin-destination matrices, which contain the complete information on commuting flows, but are difficult to analyze and compare. We propose here a versatile method, which extracts a coarse-grained signature of mobility networks, under the form of a 2 x 2 matrix that separates the flows into four categories. We apply this method to origin-destination matrices extracted from mobile phone data recorded in 31 Spanish cities. We show that these cities essentially differ by their proportion of two types of flows: integrated (between residential and employment hotspots) and random flows, whose importance increases with city size. Finally, the method allows the determination of categories of networks, and in the mobility case, the classification of cities according to their commuting structure.
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机译：大型，加权和定向网络的结构的清晰，简单的占用空间的提取是一个与许多应用相关的普遍问题。在始发地目的地矩阵中可以看到一个重要的示例，该矩阵包含有关通勤流的完整信息，但是很难进行分析和比较。我们在这里提出一种通用方法，该方法以2 x 2矩阵的形式提取移动网络的粗粒度签名，该矩阵将流量分为四个类别。我们将此方法应用于从31个西班牙城市中记录的手机数据中提取的起点-目的地矩阵。我们表明，这些城市本质上在两种流量的比例上有所不同：综合流量（居住和就业热点之间）和随机流量，其重要性随城市规模而增加。最后，该方法允许确定网络的类别，并且在移动性的情况下，可以根据城市的通勤结构确定城市的类别。
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