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Characterizing Similarity Structure of Spatial Networks Based on Degree Mixing Patterns

We address a problem of classifying and characterizing spatial networks in terms of local connection patterns of node degrees, by especially focusing on the property that the maximum node degrees of these networks are restricted to relatively small numbers. To this end, we propose two methods to analyze a set of such networks by 1) enumerating and counting the combinations of node degrees with respect to connected pair or triple nodes, 2) calculating feature vectors of these networks, which express distributions of mixing patterns' Z scores, and 3) constructing a dendrogram of these networks based on a cosine similarity between these feature vectors. In our experiments using spatial networks constructed from urban streets of seventeen cities, we confirm that our method can produce intuitively interpretable results which reflect regional characteristics of these cities. Moreover, we show that these characteristics can be reasonably described in terms of a relatively small number of selected mixing patterns, as main building blocks of given spatial networks.