Add edge betweenness centrality (#799)

* Add edge betweenness centrality

* Fix MSRV

* Update pyfunction signatures

* Add tests

* Add test with stable graph

* Remove unnecessary import from doc test

* Address review comments

---------

Co-authored-by: Ivan Carvalho <8753214+IvanIsCoding@users.noreply.github.com>
Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>

docs/source/api.rst

@@ -320,6 +320,7 @@ the functions from the explicitly typed based on the data type.
    rustworkx.digraph_spring_layout
    rustworkx.digraph_num_shortest_paths_unweighted
    rustworkx.digraph_betweenness_centrality
+   rustworkx.digraph_edge_betweenness_centrality
    rustworkx.digraph_eigenvector_centrality
    rustworkx.digraph_unweighted_average_shortest_path_length
    rustworkx.digraph_bfs_search
@@ -374,6 +375,7 @@ typed API based on the data type.
    rustworkx.graph_spring_layout
    rustworkx.graph_num_shortest_paths_unweighted
    rustworkx.graph_betweenness_centrality
+   rustworkx.graph_edge_betweenness_centrality
    rustworkx.graph_eigenvector_centrality
    rustworkx.graph_unweighted_average_shortest_path_length
    rustworkx.graph_bfs_search
@@ -416,6 +418,7 @@ Custom Return Types
    rustworkx.AllPairsPathMapping
    rustworkx.AllPairsPathLengthMapping
    rustworkx.CentralityMapping
+   rustworkx.EdgeCentralityMapping
    rustworkx.Chains
    rustworkx.NodeMap
    rustworkx.ProductNodeMap

releasenotes/notes/add-edge-betweenness-centrality-8de06bf716caece0.yaml

@@ -0,0 +1,39 @@
+---
+features:
+  - |
+    Added a new function, :func:`~rustworkx.edge_betweenness_centrality` to compute
+    edge betweenness centrality of all edges in a :class:`~rustworkx.PyGraph` or
+    :class:`~rustworkx.PyDiGraph` object. The algorithm used in this function is
+    based on:
+    Ulrik Brandes, On Variants of Shortest-Path Betweenness Centrality
+    and their Generic Computation. Social Networks 30(2):136-145, 2008.
+    Edge betweenness centrality of an edge :math:`e` is the sum of the
+    fraction of all-pairs shortest paths that pass through :math`e`
+    
+    .. math::
+  
+       c_B(e) =\sum_{s,t \in V} \frac{\sigma(s, t|e)}{\sigma(s, t)}
+  
+    where :math:`V` is the set of nodes, :math:`\sigma(s, t)` is the
+    number of shortest :math:`(s, t)`-paths, and :math:`\sigma(s, t|e)` is
+    the number of those paths passing through edge :math:`e`.
+    For example, the following computes the edge betweenness centrality for all
+    edges in a 5x5 grid graph and uses the result to color the edges in a graph
+    visualization:
+    
+    .. jupyter-execute::
+    
+      import rustworkx
+      from rustworkx.visualization import mpl_draw
+      
+      graph = rustworkx.generators.grid_graph(5, 5)
+      btw = rustworkx.edge_betweenness_centrality(graph)
+      # Color edges in graph visualization with edge betweenness centrality
+      colors = []
+      for i in graph.edge_indices():
+          colors.append(btw[i])
+      mpl_draw(graph, edge_color=colors)
+  - |
+    Added a new function to rustworkx-core ``edge_betweenness_centrality`` to
+    the ``rustworkx_core:centrality`` module which computes the edge betweenness
+    centrality of all edges in a given graph.

rustworkx-core/Cargo.toml

@@ -17,6 +17,7 @@ petgraph = "0.6.3"
 rayon = "1.6"
 num-traits = "0.2"
 priority-queue = "1.2"
+rayon-cond = "0.2"
 
 [dependencies.hashbrown]
 version = "0.12"