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<p class="admonition-title">Note</p>
<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-geospatial-plot-polygons-py"><span class="std std-ref">here</span></a>
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<section class="sphx-glr-example-title" id="graphs-from-polygons">
<span id="sphx-glr-auto-examples-geospatial-plot-polygons-py"></span><h1>Graphs from Polygons<a class="headerlink" href="#graphs-from-polygons" title="Permalink to this heading">#</a></h1>
<p>This example shows how to build a graph from a set of polygons
using PySAL and geopandas. We’ll focus on the Queen contiguity
graph, but constructors are also provided for Rook contiguity,
as well as other kinds of graphs from the polygon centroids.</p>
<img src="../../_images/sphx_glr_plot_polygons_001.png" srcset="../../_images/sphx_glr_plot_polygons_001.png" alt="plot polygons" class = "sphx-glr-single-img"/><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">libpysal</span> <span class="kn">import</span> <span class="n">weights</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">networkx</span> <span class="k">as</span> <span class="nn">nx</span>
<span class="kn">import</span> <span class="nn">geopandas</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="c1"># read in example data from geojson. GeoJSON is a file format</span>
<span class="c1"># for encoding geographic data based on JSON. It is useful for</span>
<span class="c1"># presenting geographic data on the web, and is increasingly</span>
<span class="c1"># used as a file format for geographic data.</span>
<a href="https://docs.python.org/3/library/stdtypes.html#str" title="builtins.str" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">filepath</span></a> <span class="o">=</span> <span class="s2">"nuts1.geojson"</span>
<a href="https://geopandas.org/en/stable/docs/reference/api/geopandas.GeoDataFrame.html#geopandas.GeoDataFrame" title="geopandas.GeoDataFrame" class="sphx-glr-backref-module-geopandas sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">european_regions</span></a> <span class="o">=</span> <a href="https://geopandas.org/en/stable/docs/reference/api/geopandas.read_file.html#geopandas.read_file" title="geopandas.read_file" class="sphx-glr-backref-module-geopandas sphx-glr-backref-type-py-function"><span class="n">geopandas</span><span class="o">.</span><span class="n">read_file</span></a><span class="p">(</span><a href="https://docs.python.org/3/library/stdtypes.html#str" title="builtins.str" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">filepath</span></a><span class="p">)</span>
<span class="c1"># extract the centroids for connecting the regions, which is</span>
<span class="c1"># the average of the coordinates that define the polygon's boundary</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">centroids</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.column_stack.html#numpy.column_stack" title="numpy.column_stack" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">column_stack</span></a><span class="p">((</span><a href="https://geopandas.org/en/stable/docs/reference/api/geopandas.GeoDataFrame.html#geopandas.GeoDataFrame" title="geopandas.GeoDataFrame" class="sphx-glr-backref-module-geopandas sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">european_regions</span></a><span class="o">.</span><span class="n">centroid</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <a href="https://geopandas.org/en/stable/docs/reference/api/geopandas.GeoDataFrame.html#geopandas.GeoDataFrame" title="geopandas.GeoDataFrame" class="sphx-glr-backref-module-geopandas sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">european_regions</span></a><span class="o">.</span><span class="n">centroid</span><span class="o">.</span><span class="n">y</span><span class="p">))</span>
<span class="c1"># construct the "Queen" adjacency graph. In geographical applications,</span>
<span class="c1"># the "Queen" adjacency graph considers two polygons as connected if</span>
<span class="c1"># they share a single point on their boundary. This is an analogue to</span>
<span class="c1"># the "Moore" neighborhood nine surrounding cells in a regular grid.</span>
<span class="n">queen</span> <span class="o">=</span> <span class="n">weights</span><span class="o">.</span><span class="n">Queen</span><span class="o">.</span><span class="n">from_dataframe</span><span class="p">(</span><a href="https://geopandas.org/en/stable/docs/reference/api/geopandas.GeoDataFrame.html#geopandas.GeoDataFrame" title="geopandas.GeoDataFrame" class="sphx-glr-backref-module-geopandas sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">european_regions</span></a><span class="p">)</span>
<span class="c1"># Then, we can convert the graph to networkx object using the</span>
<span class="c1"># .to_networkx() method.</span>
<span class="n">graph</span> <span class="o">=</span> <span class="n">queen</span><span class="o">.</span><span class="n">to_networkx</span><span class="p">()</span>
<span class="c1"># To plot with networkx, we need to merge the nodes back to</span>
<span class="c1"># their positions in order to plot in networkx</span>
<a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">positions</span></a> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">graph</span><span class="o">.</span><span class="n">nodes</span><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">centroids</span></a><span class="p">))</span>
<span class="c1"># plot with a nice basemap</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes" title="matplotlib.axes.Axes" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span></a> <span class="o">=</span> <a href="https://geopandas.org/en/stable/docs/reference/api/geopandas.GeoDataFrame.html#geopandas.GeoDataFrame" title="geopandas.GeoDataFrame" class="sphx-glr-backref-module-geopandas sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">european_regions</span></a><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">linewidth</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s2">"grey"</span><span class="p">,</span> <span class="n">facecolor</span><span class="o">=</span><span class="s2">"lightblue"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.axis.html#matplotlib.axes.Axes.axis" title="matplotlib.axes.Axes.axis" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">axis</span></a><span class="p">([</span><span class="o">-</span><span class="mi">12</span><span class="p">,</span> <span class="mi">45</span><span class="p">,</span> <span class="mi">33</span><span class="p">,</span> <span class="mi">66</span><span class="p">])</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.axis.html#matplotlib.axes.Axes.axis" title="matplotlib.axes.Axes.axis" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
<span class="n">nx</span><span class="o">.</span><span class="n">draw</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">positions</span></a><span class="p">,</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes" title="matplotlib.axes.Axes" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span></a><span class="o">=</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes" title="matplotlib.axes.Axes" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax</span></a><span class="p">,</span> <span class="n">node_size</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">node_color</span><span class="o">=</span><span class="s2">"r"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
<span class="c1"># An alternative method to construct graphs from polygons may use</span>
<span class="c1"># pygeos. This package is a high-performance interface to the GEOS C</span>
<span class="c1"># library, used in computing geographical relationships. These let us</span>
<span class="c1"># describe the relationships between "point sets," like polygons whether</span>
<span class="c1"># or not a line "crosses" a polygon, or whether two polygons "touch."</span>
<span class="c1"># These relationships, called "predicates", are extensive, and are documented</span>
<span class="c1"># by the pygeos package.</span>
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