美国各郡间的连通性

构建美国各郡间的连通图.

提取美国大陆相连的州的所有郡的列表.

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Length[counties = Flatten[EntityClass["AdministrativeDivision", "ContinentalUSStates"]["Subdivisions"]]]

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加上不属于 48 个相连本土州的哥伦比亚特区.

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AppendTo[counties, Entity["AdministrativeDivision", {"DistrictOfColumbia", "DistrictOfColumbia", "UnitedStates"}]];

计算与每个郡边界相连的郡的列表.

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bordering = EntityValue[counties, "BorderingCounties"];

除去无法获取边界信息的郡.

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Length[missingpos = Position[bordering, _Missing]]

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counties = Delete[counties, missingpos]; bordering = Delete[bordering, missingpos];

构建美国各郡的连通图.

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Length[edges = DeleteDuplicates[ Sort /@ Flatten[ MapThread[Thread[UndirectedEdge[##]] &, {counties, bordering}]]]]

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Graph[counties, edges]

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为构建更常见的嵌入图，下载所有郡的中心位置.

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pos = GeoPosition[EntityValue[counties, "Position"]]

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使用以下地图投影.

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proj = {"LambertAzimuthal", "Centering" -> Entity["City", {"Topeka", "Kansas", "UnitedStates"}]};

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projpos = First@GeoGridPosition[pos, proj];

现在有以下嵌入图.

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graph = Graph[counties, edges, VertexCoordinates -> projpos]

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从旧金山郡到曼哈顿，你需要访问最少 67 个郡，包括起点和终点.

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Length[path = FindShortestPath[graph, Entity[ "AdministrativeDivision", {"SanFranciscoCounty", "California", "UnitedStates"}], Entity[ "AdministrativeDivision", {"NewYorkCounty", "NewYork", "UnitedStates"}]]]

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HighlightGraph[graph, PathGraph[path]]

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