Generalizing Closeness centrality to weighted networks using Newman method (#1385)

* Add `Closeness` centrality to weighted networks using newman method

Signed-off-by: FedericoBruzzone <[email protected]>

* Test by using `assert_almost_equal!`

Signed-off-by: FedericoBruzzone <[email protected]>

* Make available `weighted_closeness` for python users

Signed-off-by: FedericoBruzzone <[email protected]>

* Fix typo in some files

Signed-off-by: FedericoBruzzone <[email protected]>

* Add docs and update `pyi` files

Signed-off-by: FedericoBruzzone <[email protected]>

* Minor fix

Signed-off-by: FedericoBruzzone <[email protected]>

* Add `releasenote`

Signed-off-by: FedericoBruzzone <[email protected]>

* Update rustworkx-core/src/centrality.rs

---------

Signed-off-by: FedericoBruzzone <[email protected]>
Co-authored-by: Ivan Carvalho <[email protected]>

Author: FedericoBruzzone

.gitignore

@@ -23,3 +23,4 @@ retworkx/*pyd
 **/*.so
 retworkx-core/Cargo.lock
 **/.DS_Store
+venv/

docs/source/api/algorithm_functions/centrality.rst

@@ -12,5 +12,6 @@ Centrality
    rustworkx.eigenvector_centrality
    rustworkx.katz_centrality
    rustworkx.closeness_centrality
+   rustworkx.newman_weighted_closeness_centrality
    rustworkx.in_degree_centrality
-   rustworkx.out_degree_centrality
+   rustworkx.out_degree_centrality

docs/source/api/pydigraph_api_functions.rst

@@ -51,6 +51,7 @@ the functions from the explicitly typed based on the data type.
    rustworkx.digraph_betweenness_centrality
    rustworkx.digraph_edge_betweenness_centrality
    rustworkx.digraph_closeness_centrality
+   rustworkx.digraph_newman_weighted_closeness_centrality
    rustworkx.digraph_eigenvector_centrality
    rustworkx.digraph_katz_centrality
    rustworkx.digraph_unweighted_average_shortest_path_length

docs/source/api/pygraph_api_functions.rst

@@ -52,6 +52,7 @@ typed API based on the data type.
    rustworkx.graph_betweenness_centrality
    rustworkx.graph_edge_betweenness_centrality
    rustworkx.graph_closeness_centrality
+   rustworkx.graph_newman_weighted_closeness_centrality
    rustworkx.graph_eigenvector_centrality
    rustworkx.graph_katz_centrality
    rustworkx.graph_unweighted_average_shortest_path_length

releasenotes/notes/newman-weighted-closeness-centrality-d4dba79712e9ac42.yaml

@@ -0,0 +1,19 @@
+---
+features:
+  - |
+    Added a new function, :func:`~.newman_weighted_closeness_centrality` to compute the
+    closeness centrality of all nodes in a weighted :class:`~.PyGraph` or
+    :class:`~.PyDiGraph` object.
+
+    The weighted closeness centrality is an extension of the standard closeness
+    centrality measure where edge weights represent connection strength rather
+    than distance. To properly compute shortest paths, weights are inverted
+    so that stronger connections correspond to shorter effective distances.
+    The algorithm follows the method described by Newman (2001) in analyzing
+    weighted graphs.
+
+    The edges originally represent connection strength between nodes.
+    The idea is that if two nodes have a strong connection, the computed
+    distance between them should be small (shorter), and vice versa.
+    Note that this assume that the graph is modelling a measure of
+    connection strength (e.g. trust, collaboration, or similarity).