voronoi_cells#
- voronoi_cells(G, center_nodes, weight='weight')[source]#
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 â€śoutwardâ€ť Voronoi cells, as defined in [1], in which distance is measured from the center nodes to the target node. For the â€śinwardâ€ť Voronoi cells, use the
DiGraph.reverse()
method to reverse the orientation of the edges before invoking this function on the directed graph.- Parameters:
- GNetworkX graph
- center_nodesset
A nonempty set of nodes in the graph
G
that represent the center of the Voronoi cells.- weightstring 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 ofG
.
- Raises:
- ValueError
If
center_nodes
is empty.
References
[1] (1,2)Erwig, Martin. (2000),â€ťThe graph Voronoi diagram with applications.â€ť Networks, 36: 156â€“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]]