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# voronoi_cells

voronoi_cells(G, center_nodes, weight='weight')

  Returns the Voronoi cells centered at `center_nodes` with respect to the shortest-path distance metric.

  If \(C\) is a set of nodes in the graph and \(c\) is an element of \(C\), the Voronoi cell centered at a node \(c\) is the set of all nodes \(v\) that are closer to \(c\) than to any other center node in \(C\) with respect to the shortest-path distance metric. [1]

  For directed graphs, this will compute the “outward” Voronoi cells, as defined in [1], in which distance is measured from the center nodes to the target node. For the “inward” Voronoi cells, use the `DiGraph.reverse()` method to reverse the orientation of the edges before invoking this function on the directed graph.

  Parameters:
    G NetworkX graph
    center_nodes set

      A nonempty set of nodes in the graph `G` that represent the center of the Voronoi cells.

    weight string or function

      The edge attribute (or an arbitrary function) representing the weight of an edge. This keyword argument is as described in the documentation for `multi_source_dijkstra_path()`, for example.

  Returns:
    dictionary

      A mapping from center node to set of all nodes in the graph closer to that center node than to any other center node. The keys of the dictionary are the element of `center_nodes`, and the values of the dictionary form a partition of the nodes of `G`.

  Raises:
    ValueError

      If `center_nodes` is empty.

  References

  [1] (1,2)

  Erwig, Martin. (2000),”The graph Voronoi diagram with applications.” Networks, 36: 156–163. https://doi.org/10.1002/1097-0037(200010)36:3<156::AID-NET2>3.0.CO;2-L

  Examples

  To get only the partition of the graph induced by the Voronoi cells, take the collection of all values in the returned dictionary:

      >>> G = nx.path_graph(6)
      >>> center_nodes = {0, 3}
      >>> cells = nx.voronoi_cells(G, center_nodes)
      >>> partition = set(map(frozenset, cells.values()))
      >>> sorted(map(sorted, partition))
      [[0, 1], [2, 3, 4, 5]]