ethod to find the mean-centered coordinates of the vertices in the graph.</span>

<span class="sd">        Returns:</span>
<span class="sd">            dict: A dictionary mapping vertices to their mean-centered coordinates.</span>

<span class="sd">        &quot;&quot;&quot;</span>
        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">coordinates</span><span class="p">:</span>
            <span class="k">return</span> <span class="k