Implementation of cycle_basis_edges

docs/source/api/algorithm_functions/connectivity_and_cycles.rst

@@ -17,6 +17,7 @@ Connectivity and Cycles
    rustworkx.weakly_connected_components
    rustworkx.is_weakly_connected
    rustworkx.cycle_basis
+   rustworkx.cycle_basis_edges
    rustworkx.simple_cycles
    rustworkx.digraph_find_cycle
    rustworkx.articulation_points

releasenotes/notes/add-cycle-basis-edges-5cb31eac7e41096d.yaml

@@ -0,0 +1,56 @@
+---
+features:
+  - |
+    A function, ``cycle_basis_edges`` was added to the crate
+    ``rustworkx-core`` in the ``connectivity`` module. This function returns 
+    the edge indices that form the cycle basis of a graph.
+  - |
+    Added a new function :func:`~rustworkx.cycle_basis_edges`  which is similar
+    to the existing :func:`~.cycle_basis` function but instead of returning node
+    indices it returns a list of edge indices for the cycle.
+
+    .. jupyter-execute::
+
+      import rustworkx
+      from rustworkx.visualization import * # Needs matplotlib/
+
+      graph = rustworkx.PyGraph()
+
+      # Each time add node is called, it returns a new node index
+      a = graph.add_node("A")
+      b = graph.add_node("B")
+      c = graph.add_node("C")
+      d = graph.add_node("D")
+      e = graph.add_node("E")
+      f = graph.add_node("F")
+      g = graph.add_node("G")
+      h = graph.add_node("H")
+      i = graph.add_node("I")
+      j = graph.add_node("J")
+
+      # add_edges_from takes tuples of node indices and weights,
+      # and returns edge indices
+      graph.add_edges_from([
+          (a, b, 1.5), 
+          (a, a, 1.0), 
+          (a, c, 5.0), 
+          (b, c, 2.5), 
+          (c, d, 1.3), 
+          (d, e, 0.8), 
+          (e, f, 1.6), 
+          (f, d, 0.7), 
+          (e, g, 0.7), 
+          (g, h, 0.9), 
+          (g, i, 1.0), 
+          (i, j, 0.8),
+      ])
+
+      mpl_draw(graph, with_labels=True)
+      # Retrieve EdgeIDs by enabling the edges flag.
+      cycles_edges = rustworkx.cycle_basis_edges(graph, a)
+      edge_list = list(graph.edge_list())
+      cycle_info = [[graph.get_edge_data_by_index(edge) for edge in cycle] for cycle in cycles_edges]
+      # Print the EdgeID's that form cycles in the graph
+      display(cycles_edges)
+      # Print the data retrieved from the graph.
+      display(cycle_info)

rustworkx-core/src/connectivity/cycle_basis.rs

@@ -11,10 +11,12 @@
 // under the License.
 
 use hashbrown::{HashMap, HashSet};
-use petgraph::visit::{IntoNeighbors, IntoNodeIdentifiers, NodeCount};
+use petgraph::visit::{EdgeRef, IntoEdges, IntoNeighbors, IntoNodeIdentifiers, NodeCount};
 use std::hash::Hash;
 
-/// Return a list of cycles which form a basis for cycles of a given graph.
+/// Inner private function for `cycle_basis` and `cycle_basis_edges`.
+/// Returns a list of cycles which forms a basis of cycles of a given
+/// graph.
 ///
 /// A basis for cycles of a graph is a minimal collection of
 /// cycles such that any cycle in the graph can be written
@@ -29,32 +31,32 @@ use std::hash::Hash;
 /// It may produce incorrect/unexpected results if the input graph has
 /// parallel edges.
 ///
-///
 /// Arguments:
 ///
 /// * `graph` - The graph in which to find the basis.
 /// * `root` - Optional node index for starting the basis search. If not
 ///   specified, an arbitrary node is chosen.
-///
-/// # Example
-/// ```rust
-/// use petgraph::prelude::*;
-/// use rustworkx_core::connectivity::cycle_basis;
-///
-/// let edge_list = [(0, 1), (0, 3), (0, 5), (1, 2), (2, 3), (3, 4), (4, 5)];
-/// let graph = UnGraph::<i32, i32>::from_edges(&edge_list);
-/// let mut res: Vec<Vec<NodeIndex>> = cycle_basis(&graph, Some(NodeIndex::new(0)));
-/// ```
-pub fn cycle_basis<G>(graph: G, root: Option<G::NodeId>) -> Vec<Vec<G::NodeId>>
+/// * `self_cycle_builder` - Specifies the behavior when a single node cycle
+///   is found.
+/// * `cycle_builder` - Specifies the behavior when a cycle is found
+fn inner_cycle_basis<G, T, F>(
+    graph: G,
+    root: Option<G::NodeId>,
+    self_cycle_builder: impl Fn(G, G::NodeId) -> Vec<T>,
+    cycle_builder: F,
+) -> Vec<Vec<T>>
 where
     G: NodeCount,
     G: IntoNeighbors,
     G: IntoNodeIdentifiers,
+    T: Eq + Hash,
     G::NodeId: Eq + Hash,
+    F: Fn(G, &HashSet<G::NodeId>, &HashMap<G::NodeId, G::NodeId>, G::NodeId, G::NodeId) -> Vec<T>,
 {
-    let mut root_node = root;
+    let mut root_node: Option<G::NodeId> = root;
     let mut graph_nodes: HashSet<G::NodeId> = graph.node_identifiers().collect();
-    let mut cycles: Vec<Vec<G::NodeId>> = Vec::new();
+    let mut cycles: Vec<Vec<T>> = Vec::new();
+
     while !graph_nodes.is_empty() {
         let temp_value: G::NodeId;
         // If root_node is not set get an arbitrary node from the set of graph
@@ -88,20 +90,12 @@ where
                     used.insert(neighbor, temp_set);
                 // A self loop:
                 } else if z == neighbor {
-                    let cycle: Vec<G::NodeId> = vec![z];
-                    cycles.push(cycle);
+                    cycles.push(self_cycle_builder(graph, z))
                 // A cycle was found:
                 } else if !used.get(&z).unwrap().contains(&neighbor) {
                     let prev_n = used.get(&neighbor).unwrap();
-                    let mut cycle: Vec<G::NodeId> = vec![neighbor, z];
-                    let mut p = pred.get(&z).unwrap();
-                    while !prev_n.contains(p) {
-                        cycle.push(*p);
-                        p = pred.get(p).unwrap();
-                    }
-                    cycle.push(*p);
-                    cycles.push(cycle);
-                    let neighbor_set = used.get_mut(&neighbor).unwrap();
+                    cycles.push(cycle_builder(graph, prev_n, &pred, z, neighbor));
+                    let neighbor_set: &mut HashSet<G::NodeId> = used.get_mut(&neighbor).unwrap();
                     neighbor_set.insert(z);
                 }
             }
@@ -116,15 +110,162 @@ where
     cycles
 }
 
+/// Returns lists of `NodeIndex` representing cycles which form
+/// a basis for cycles of a given graph.
+///
+/// A basis for cycles of a graph is a minimal collection of
+/// cycles such that any cycle in the graph can be written
+/// as a sum of cycles in the basis.  Here summation of cycles
+/// is defined as the exclusive-or of the edges.
+///
+/// This is adapted from
+///    Paton, K. An algorithm for finding a fundamental set of
+///    cycles of a graph. Comm. ACM 12, 9 (Sept 1969), 514-518.
+///
+/// The function implicitly assumes that there are no parallel edges.
+/// It may produce incorrect/unexpected results if the input graph has
+/// parallel edges.
+///
+/// Arguments:
+///
+/// * `graph` - The graph in which to find the basis.
+/// * `root` - Optional node index for starting the basis search. If not
+///   specified, an arbitrary node is chosen.
+///
+/// # Example
+/// ```rust
+/// use petgraph::prelude::*;
+/// use rustworkx_core::connectivity::cycle_basis;
+///
+/// let edge_list = [(0, 1), (0, 3), (0, 5), (1, 2), (2, 3), (3, 4), (4, 5)];
+/// let graph = UnGraph::<i32, i32>::from_edges(&edge_list);
+/// let mut res: Vec<Vec<NodeIndex>> = cycle_basis(&graph, Some(NodeIndex::new(0)));
+/// ```
+pub fn cycle_basis<G>(graph: G, root: Option<G::NodeId>) -> Vec<Vec<G::NodeId>>
+where
+    G: NodeCount,
+    G: IntoNeighbors,
+    G: IntoNodeIdentifiers,
+    G::NodeId: Eq + Hash,
+{
+    let self_cycle_builder = |_graph: G, node: G::NodeId| -> Vec<G::NodeId> { vec![node] };
+    let cycle_builder = |_graph: G,
+                         prev_n: &HashSet<G::NodeId>,
+                         pred_to_node: &HashMap<G::NodeId, G::NodeId>,
+                         origin: G::NodeId,
+                         neighbor: G::NodeId|
+     -> Vec<G::NodeId> {
+        let mut p = pred_to_node.get(&origin).unwrap();
+        // Append neighbor and z to cycle.
+        let mut cycle: Vec<G::NodeId> = vec![neighbor, origin];
+        while !prev_n.contains(p) {
+            cycle.push(*p);
+            p = pred_to_node.get(p).unwrap();
+        }
+        cycle.push(*p);
+        cycle
+    };
+    inner_cycle_basis(graph, root, self_cycle_builder, cycle_builder)
+}
+
+/// Returns lists of `EdgeIndex` representing cycles which form
+/// a basis for cycles of a given graph.
+///
+/// A basis for cycles of a graph is a minimal collection of
+/// cycles such that any cycle in the graph can be written
+/// as a sum of cycles in the basis.  Here summation of cycles
+/// is defined as the exclusive-or of the edges.
+///
+/// This is adapted from
+///    Paton, K. An algorithm for finding a fundamental set of
+///    cycles of a graph. Comm. ACM 12, 9 (Sept 1969), 514-518.
+///
+/// The function implicitly assumes that there are no parallel edges.
+/// It may produce incorrect/unexpected results if the input graph has
+/// parallel edges.
+///
+/// Arguments:
+///
+/// * `graph` - The graph in which to find the basis.
+/// * `root` - Optional node index for starting the basis search. If not
+///   specified, an arbitrary node is chosen.
+///
+/// # Example
+/// ```rust
+/// use petgraph::prelude::*;
+/// use rustworkx_core::connectivity::cycle_basis_edges;
+///
+/// let edge_list = [(0, 1), (0, 3), (0, 5), (1, 2), (2, 3), (3, 4), (4, 5)];
+/// let graph = UnGraph::<i32, i32>::from_edges(&edge_list);
+/// let mut res: Vec<Vec<EdgeIndex>> = cycle_basis_edges(&graph, Some(NodeIndex::new(0)));
+/// ```
+pub fn cycle_basis_edges<G>(graph: G, root: Option<G::NodeId>) -> Vec<Vec<G::EdgeId>>
+where
+    G: NodeCount,
+    G: IntoEdges,
+    G: IntoNodeIdentifiers,
+    G::NodeId: Eq + Hash,
+    G::EdgeId: Eq + Hash,
+{
+    /// Method used to retrieve all the edges between an origin node and a target node.
+    fn get_edge_between<G>(orig_graph: G, origin: G::NodeId, target: G::NodeId) -> G::EdgeId
+    where
+        G: IntoEdges,
+    {
+        orig_graph
+            .edges(origin)
+            .filter_map(|edge: G::EdgeRef| (edge.target() == target).then_some(edge.id()))
+            .next()
+            .expect("An edge should exist between origin and target node")
+    }
+
+    let self_cycle_builder =
+        |graph: G, node: G::NodeId| -> Vec<G::EdgeId> { vec![get_edge_between(graph, node, node)] };
+    let cycle_builder = |graph: G,
+                         prev_n: &HashSet<G::NodeId>,
+                         pred_to_node: &HashMap<G::NodeId, G::NodeId>,
+                         origin: G::NodeId,
+                         neighbor: G::NodeId|
+     -> Vec<G::EdgeId> {
+        let mut p = pred_to_node.get(&origin).unwrap();
+        let mut cycle: Vec<G::EdgeId> = Vec::new();
+        // Retrieve all edges from z to neighbor and push to cycle
+        cycle.push(get_edge_between(graph, origin, neighbor));
+
+        // Make last p_node == z
+        let mut prev_p: &G::NodeId = &origin;
+        // While p is in the neighborhood of neighbor
+        while !prev_n.contains(p) {
+            // Retrieve all edges from prev_p to p and vice versa append to cycle
+            cycle.push(get_edge_between(graph, *prev_p, *p));
+            // Update prev_p to p
+            prev_p = p;
+            // Retrieve a new predecessor node from p and replace p
+            p = pred_to_node.get(p).unwrap();
+        }
+        // When loop ends add remaining edges from prev_p to p.
+        cycle.push(get_edge_between(graph, *prev_p, *p));
+        // Also retrieve all edges between the last p and neighbor
+        cycle.push(get_edge_between(graph, *p, neighbor));
+        cycle
+    };
+    inner_cycle_basis(graph, root, self_cycle_builder, cycle_builder)
+}
+
 #[cfg(test)]
 mod tests {
     use crate::connectivity::cycle_basis;
+    use crate::connectivity::cycle_basis_edges;
     use petgraph::prelude::*;
+    use petgraph::stable_graph::GraphIndex;
 
-    fn sorted_cycle(cycles: Vec<Vec<NodeIndex>>) -> Vec<Vec<usize>> {
+    fn sorted_cycle<T>(cycles: Vec<Vec<T>>) -> Vec<Vec<usize>>
+    where
+        T: GraphIndex,
+    {
         let mut sorted_cycles: Vec<Vec<usize>> = vec![];
         for cycle in cycles {
-            let mut cycle: Vec<usize> = cycle.iter().map(|x| x.index()).collect();
+            let mut cycle: Vec<usize> = cycle.iter().map(|x: &T| x.index()).collect();
             cycle.sort();
             sorted_cycles.push(cycle);
         }
@@ -158,6 +299,28 @@ mod tests {
         assert_eq!(sorted_cycle(res_9), expected);
     }
 
+    #[test]
+    fn test_cycle_edge_basis_source() {
+        let edge_list = vec![
+            (0, 0),
+            (0, 1),
+            (1, 2),
+            (2, 3),
+            (2, 5),
+            (5, 6),
+            (3, 6),
+            (3, 4),
+        ];
+        let graph = UnGraph::<i32, i32>::from_edges(&edge_list);
+        let expected = vec![vec![0], vec![3, 4, 5, 6]];
+        let res_0 = cycle_basis_edges(&graph, Some(NodeIndex::new(0)));
+        assert_eq!(sorted_cycle(res_0), expected);
+        let res_1 = cycle_basis_edges(&graph, Some(NodeIndex::new(2)));
+        assert_eq!(sorted_cycle(res_1), expected);
+        let res_9 = cycle_basis_edges(&graph, Some(NodeIndex::new(6)));
+        assert_eq!(sorted_cycle(res_9), expected);
+    }
+
     #[test]
     fn test_self_loop() {
         let edge_list = vec![
@@ -187,4 +350,34 @@ mod tests {
             ]
         );
     }
+
+    #[test]
+    fn test_self_loop_edges() {
+        let edge_list = vec![
+            (0, 1),
+            (0, 3),
+            (0, 5),
+            (0, 8),
+            (1, 2),
+            (1, 6),
+            (2, 3),
+            (3, 4),
+            (4, 5),
+            (6, 7),
+            (7, 8),
+            (8, 9),
+        ];
+        let mut graph = UnGraph::<i32, i32>::from_edges(&edge_list);
+        graph.add_edge(NodeIndex::new(1), NodeIndex::new(1), 0);
+        let res_0 = cycle_basis_edges(&graph, Some(NodeIndex::new(0)));
+        assert_eq!(
+            sorted_cycle(res_0),
+            vec![
+                vec![0, 1, 4, 6],
+                vec![0, 3, 5, 9, 10],
+                vec![1, 2, 7, 8],
+                vec![12],
+            ]
+        );
+    }
 }

rustworkx-core/src/connectivity/mod.rs

@@ -34,6 +34,7 @@ pub use conn_components::connected_components;
 pub use conn_components::number_connected_components;
 pub use core_number::core_number;
 pub use cycle_basis::cycle_basis;
+pub use cycle_basis::cycle_basis_edges;
 pub use find_cycle::find_cycle;
 pub use isolates::isolates;
 pub use johnson_simple_cycles::{SimpleCycleIter, johnson_simple_cycles};

rustworkx/__init__.pyi

@@ -101,6 +101,7 @@ from .rustworkx import weakly_connected_components as weakly_connected_component
 from .rustworkx import digraph_adjacency_matrix as digraph_adjacency_matrix
 from .rustworkx import graph_adjacency_matrix as graph_adjacency_matrix
 from .rustworkx import cycle_basis as cycle_basis
+from .rustworkx import cycle_basis_edges as cycle_basis_edges
 from .rustworkx import articulation_points as articulation_points
 from .rustworkx import bridges as bridges
 from .rustworkx import biconnected_components as biconnected_components