Implementation of closeness_centrality (#593)

* Initial implementation of closeness_centrality

* fix typo

* add tests

* apply the suggestions.

* add a releasenote and improve Doc

* apply the suggestions

* supports rust version 1.48.0

* improve variable name

* Fix up docstrings and release note

* Fix rustworkx-core tests

---------

Co-authored-by: Matthew Treinish <[email protected]>

docs/source/api.rst

@@ -48,13 +48,15 @@ Shortest Paths
 .. _centrality:
 
 Centrality
---------------
+----------
 
 .. autosummary::
    :toctree: apiref
 
    rustworkx.betweenness_centrality
+   rustworkx.edge_betweenness_centrality
    rustworkx.eigenvector_centrality
+   rustworkx.closeness_centrality
 
 .. _traversal:
 
@@ -321,6 +323,7 @@ the functions from the explicitly typed based on the data type.
    rustworkx.digraph_num_shortest_paths_unweighted
    rustworkx.digraph_betweenness_centrality
    rustworkx.digraph_edge_betweenness_centrality
+   rustworkx.digraph_closeness_centrality
    rustworkx.digraph_eigenvector_centrality
    rustworkx.digraph_unweighted_average_shortest_path_length
    rustworkx.digraph_bfs_search
@@ -376,6 +379,7 @@ typed API based on the data type.
    rustworkx.graph_num_shortest_paths_unweighted
    rustworkx.graph_betweenness_centrality
    rustworkx.graph_edge_betweenness_centrality
+   rustworkx.graph_closeness_centrality
    rustworkx.graph_eigenvector_centrality
    rustworkx.graph_unweighted_average_shortest_path_length
    rustworkx.graph_bfs_search

releasenotes/notes/closeness-centrality-459c5c7e35cb2e63.yaml

@@ -0,0 +1,42 @@
+---
+features:
+  - |
+    Added a new function, :func:`~.closeness_centrality` to compute the
+    closeness centrality of all nodes in a :class:`~.PyGraph` or
+    :class:`~.PyDiGraph` object.
+
+    The closeness centrality of a node :math:`u` is defined as the the
+    reciprocal of the average shortest path distance to :math:`u` over all
+    :math:`n-1` reachable nodes. In it's general form this can be expressed as:
+
+    .. math::
+
+        C(u) = \frac{n - 1}{\sum_{v=1}^{n-1} d(v, u)},
+
+    where :math:`d(v, u)` is the shortest-path distance between :math:`v` and
+    :math:`u`, and :math:`n` is the number of nodes that can reach :math:`u`.
+    For example, to visualize the closeness centrality of a graph:
+
+    .. jupyter-execute::
+
+        import matplotlib.pyplot as plt
+
+        import rustworkx as rx
+        from rustworkx.visualization import mpl_draw
+
+        graph = rx.generators.hexagonal_lattice_graph(4, 4)
+        centrality = rx.closeness_centrality(graph)
+        # Generate a color list
+        colors = []
+        for node in graph.node_indices():
+            colors.append(centrality[node])
+        # Generate a visualization with a colorbar
+        plt.rcParams['figure.figsize'] = [15, 10]
+        ax = plt.gca()
+        sm = plt.cm.ScalarMappable(norm=plt.Normalize(
+            vmin=min(centrality.values()),
+            vmax=max(centrality.values())
+        ))
+        plt.colorbar(sm, ax=ax)
+        plt.title("Closeness Centrality of a 4 x 4 Hexagonal Lattice Graph")
+        mpl_draw(graph, node_color=colors, ax=ax)

rustworkx-core/src/centrality.rs

@@ -15,18 +15,22 @@ use std::hash::Hash;
 use std::sync::RwLock;
 
 use hashbrown::HashMap;
+use petgraph::algo::dijkstra;
 use petgraph::visit::{
     EdgeCount,
     EdgeIndexable,
     EdgeRef,
     GraphBase,
     GraphProp, // allows is_directed
     IntoEdges,
+    IntoEdgesDirected,
     IntoNeighbors,
     IntoNeighborsDirected,
     IntoNodeIdentifiers,
     NodeCount,
     NodeIndexable,
+    Reversed,
+    Visitable,
 };
 use rayon::prelude::*;
 use rayon_cond::CondIterator;
@@ -190,7 +194,7 @@ where
 /// Ulrik Brandes: On Variants of Shortest-Path Betweenness
 /// Centrality and their Generic Computation.
 /// Social Networks 30(2):136-145, 2008.
-/// https://doi.org/10.1016/j.socnet.2007.11.001.
+/// <https://doi.org/10.1016/j.socnet.2007.11.001>.
 ///
 /// This function is multithreaded and will run in parallel if the number
 /// of nodes in the graph is above the value of ``parallel_threshold``. If the
@@ -828,3 +832,79 @@ mod test_eigenvector_centrality {
         }
     }
 }
+
+/// Compute the closeness centrality of each node in the graph.
+///
+/// The closeness centrality of a node `u` is the reciprocal of the average
+/// shortest path distance to `u` over all `n-1` reachable nodes.
+///
+/// In the case of a graphs with more than one connected component there is
+/// an alternative improved formula that calculates the closeness centrality
+/// as "a ratio of the fraction of actors in the group who are reachable, to
+/// the average distance" [^WF]. You can enable this by setting `wf_improved` to `true`.
+///
+/// [^WF] Wasserman, S., & Faust, K. (1994). Social Network Analysis:
+///     Methods and Applications (Structural Analysis in the Social Sciences).
+///     Cambridge: Cambridge University Press. doi:10.1017/CBO9780511815478
+///
+/// Arguments:
+///
+/// * `graph` - The graph object to run the algorithm on
+/// * `wf_improved` - If `true`, scale by the fraction of nodes reachable.
+///
+/// # Example
+/// ```rust
+/// use rustworkx_core::petgraph;
+/// use rustworkx_core::centrality::closeness_centrality;
+///
+/// // Calculate the closeness centrality of Graph
+/// let g = petgraph::graph::UnGraph::<i32, ()>::from_edges(&[
+///     (0, 4), (1, 2), (2, 3), (3, 4), (1, 4)
+/// ]);
+/// let output = closeness_centrality(&g, true);
+/// assert_eq!(
+///     vec![Some(1./2.), Some(2./3.), Some(4./7.), Some(2./3.), Some(4./5.)],
+///     output
+/// );
+///
+/// // Calculate the closeness centrality of DiGraph
+/// let dg = petgraph::graph::DiGraph::<i32, ()>::from_edges(&[
+///     (0, 4), (1, 2), (2, 3), (3, 4), (1, 4)
+/// ]);
+/// let output = closeness_centrality(&dg, true);
+/// assert_eq!(
+///     vec![Some(0.), Some(0.), Some(1./4.), Some(1./3.), Some(4./5.)],
+///     output
+/// );
+/// ```
+pub fn closeness_centrality<G>(graph: G, wf_improved: bool) -> Vec<Option<f64>>
+where
+    G: NodeIndexable
+        + IntoNodeIdentifiers
+        + GraphBase
+        + IntoEdges
+        + Visitable
+        + NodeCount
+        + IntoEdgesDirected,
+    G::NodeId: std::hash::Hash + Eq,
+{
+    let max_index = graph.node_bound();
+    let mut closeness: Vec<Option<f64>> = vec![None; max_index];
+    for node_s in graph.node_identifiers() {
+        let is = graph.to_index(node_s);
+        let map = dijkstra(Reversed(&graph), node_s, None, |_| 1);
+        let reachable_nodes_count = map.len();
+        let dists_sum: usize = map.into_values().sum();
+        if reachable_nodes_count == 1 {
+            closeness[is] = Some(0.0);
+            continue;
+        }
+        closeness[is] = Some((reachable_nodes_count - 1) as f64 / dists_sum as f64);
+        if wf_improved {
+            let node_count = graph.node_count();
+            closeness[is] = closeness[is]
+                .map(|c| c * (reachable_nodes_count - 1) as f64 / (node_count - 1) as f64);
+        }
+    }
+    closeness
+}

rustworkx-core/tests/centrality.rs

@@ -0,0 +1,100 @@
+// Licensed under the Apache License, Version 2.0 (the "License"); you may
+// not use this file except in compliance with the License. You may obtain
+// a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
+// WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
+// License for the specific language governing permissions and limitations
+// under the License.
+
+use petgraph::visit::Reversed;
+use rustworkx_core::centrality::closeness_centrality;
+use rustworkx_core::petgraph::graph::{DiGraph, UnGraph};
+
+#[test]
+fn test_simple() {
+    let g = UnGraph::<i32, ()>::from_edges(&[(1, 2), (2, 3), (3, 4), (1, 4)]);
+    let c = closeness_centrality(&g, true);
+    assert_eq!(
+        vec![
+            Some(0.0),
+            Some(0.5625),
+            Some(0.5625),
+            Some(0.5625),
+            Some(0.5625)
+        ],
+        c
+    );
+}
+
+#[test]
+fn test_wf_improved() {
+    let g = UnGraph::<i32, ()>::from_edges(&[(0, 1), (1, 2), (2, 3), (4, 5), (5, 6)]);
+    let c = closeness_centrality(&g, true);
+    assert_eq!(
+        vec![
+            Some(1.0 / 4.0),
+            Some(3.0 / 8.0),
+            Some(3.0 / 8.0),
+            Some(1.0 / 4.0),
+            Some(2.0 / 9.0),
+            Some(1.0 / 3.0),
+            Some(2.0 / 9.0)
+        ],
+        c
+    );
+    let cwf = closeness_centrality(&g, false);
+    assert_eq!(
+        vec![
+            Some(1.0 / 2.0),
+            Some(3.0 / 4.0),
+            Some(3.0 / 4.0),
+            Some(1.0 / 2.0),
+            Some(2.0 / 3.0),
+            Some(1.0),
+            Some(2.0 / 3.0)
+        ],
+        cwf
+    );
+}
+
+#[test]
+fn test_digraph() {
+    let g = DiGraph::<i32, ()>::from_edges(&[(0, 1), (1, 2)]);
+    let c = closeness_centrality(&g, true);
+    assert_eq!(vec![Some(0.), Some(1. / 2.), Some(2. / 3.)], c);
+
+    let cr = closeness_centrality(Reversed(&g), true);
+    assert_eq!(vec![Some(2. / 3.), Some(1. / 2.), Some(0.)], cr);
+}
+
+#[test]
+fn test_k5() {
+    let g = UnGraph::<i32, ()>::from_edges(&[
+        (0, 1),
+        (0, 2),
+        (0, 3),
+        (0, 4),
+        (1, 2),
+        (1, 3),
+        (1, 4),
+        (2, 3),
+        (2, 4),
+        (3, 4),
+    ]);
+    let c = closeness_centrality(&g, true);
+    assert_eq!(
+        vec![Some(1.0), Some(1.0), Some(1.0), Some(1.0), Some(1.0)],
+        c
+    );
+}
+
+#[test]
+fn test_path() {
+    let g = UnGraph::<i32, ()>::from_edges(&[(0, 1), (1, 2)]);
+    let c = closeness_centrality(&g, true);
+    assert_eq!(vec![Some(2.0 / 3.0), Some(1.0), Some(2.0 / 3.0)], c);
+}

rustworkx/__init__.py

@@ -1600,9 +1600,65 @@ def _graph_betweenness_centrality(graph, normalized=True, endpoints=False, paral
     )
 
 
+@functools.singledispatch
+def closeness_centrality(graph, wf_improved=True):
+    r"""Compute the closeness centrality of each node in a graph object.
+
+    The closeness centrality of a node :math:`u` is defined as the
+    reciprocal of the average shortest path distance to :math:`u` over all
+    :math:`n-1` reachable nodes in the graph. In it's general form this can
+    be expressed as:
+
+    .. math::
+
+        C(u) = \frac{n - 1}{\sum_{v=1}^{n-1} d(v, u)},
+
+    where:
+
+      * :math:`d(v, u)` - the shortest-path distance between :math:`v` and
+        :math:`u`
+      * :math:`n` - the number of nodes that can reach :math:`u`.
+
+    In the case of a graphs with more than one connected component there is
+    an alternative improved formula that calculates the closeness centrality
+    as "a ratio of the fraction of actors in the group who are reachable, to
+    the average distance" [WF]_. This can be expressed as
+
+    .. math::
+
+        C_{WF}(u) = \frac{n-1}{N-1} \frac{n - 1}{\sum_{v=1}^{n-1} d(v, u)},
+
+    where :math:`N` is the number of nodes in the graph. This alternative
+    formula can be used with the ``wf_improved`` argument.
+
+    :param graph: The input graph. Can either be a
+        :class:`~retworkx.PyGraph` or :class:`~retworkx.PyDiGraph`.
+    :param bool wf_improved: This is optional; the default is True. If True,
+        scale by the fraction of nodes reachable.
+
+    :returns: A dictionary mapping each node index to its closeness centrality.
+    :rtype: dict
+
+    .. [WF] Wasserman, S., & Faust, K. (1994). Social Network Analysis:
+      Methods and Applications (Structural Analysis in the Social Sciences).
+      Cambridge: Cambridge University Press. doi:10.1017/CBO9780511815478
+    """
+    raise TypeError("Invalid input type %s for graph" % type(graph))
+
+
+@closeness_centrality.register(PyDiGraph)
+def _digraph_closeness_centrality(graph, wf_improved=True):
+    return digraph_closeness_centrality(graph, wf_improved=wf_improved)
+
+
+@closeness_centrality.register(PyGraph)
+def _graph_closeness_centrality(graph, wf_improved=True):
+    return graph_closeness_centrality(graph, wf_improved=wf_improved)
+
+
 @functools.singledispatch
 def edge_betweenness_centrality(graph, normalized=True, parallel_threshold=50):
-    """Compute the edge betweenness centrality of all edges in a graph.
+    r"""Compute the edge betweenness centrality of all edges in a graph.
 
     Edge betweenness centrality of an edge :math:`e` is the sum of the
     fraction of all-pairs shortest paths that pass through :math`e`
@@ -1641,6 +1697,7 @@ def edge_betweenness_centrality(graph, normalized=True, parallel_threshold=50):
         betweenness score for each node.
     :rtype: EdgeCentralityMapping
     """
+    raise TypeError("Invalid input type %s for graph" % type(graph))
 
 
 @edge_betweenness_centrality.register(PyDiGraph)