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//! `PageRank` centrality (ALGO-PR-011).
//!
//! Counterpart of `igraph_pagerank()` from
//! `references/igraph/src/centrality/pagerank.c` (the
//! `IGRAPH_PAGERANK_ALGO_POWER` branch). Implemented as standard power
//! iteration:
//!
//! `PR_new[v] = (1 - d) / N + d * (Σ_{u → v} PR[u] / out_deg(u) +
//! Σ_{sink} PR[sink] / N)`
//!
//! where the second sum handles "dangling" vertices (out-degree 0) by
//! distributing their rank uniformly across the graph.
//!
//! For undirected graphs every edge counts as bidirectional, so
//! `out_deg(u) == deg(u)` and the in-neighbour iteration is symmetric.
//!
//! Phase-1 minimal slice: undirected / `IGRAPH_OUT`, unweighted, damping
//! `0.85`, `eps = 1e-10`, `max_iter = 1000`. Configurable parameters and
//! ARPACK-based variants ship later.
use crate::core::{Graph, IgraphResult};
const DEFAULT_DAMPING: f64 = 0.85;
const DEFAULT_EPS: f64 = 1e-10;
const DEFAULT_MAX_ITER: usize = 1000;
/// `PageRank` scores via power iteration with damping `0.85`.
///
/// Returns a `Vec<f64>` summing approximately to 1. For graphs with
/// `vcount = 0` returns an empty vector.
///
/// Counterpart of
/// `igraph_pagerank(_, IGRAPH_PAGERANK_ALGO_POWER, _, _, vss_all(),
/// /*directed=*/g.is_directed(), 0.85, NULL_weights, NULL_options)`
/// with default convergence parameters.
///
/// # Examples
///
/// ```
/// use rust_igraph::{Graph, pagerank};
///
/// // Triangle: every vertex has identical PageRank ≈ 1/3.
/// let mut g = Graph::with_vertices(3);
/// g.add_edge(0, 1).unwrap();
/// g.add_edge(1, 2).unwrap();
/// g.add_edge(2, 0).unwrap();
/// let pr = pagerank(&g).unwrap();
/// assert!((pr[0] - 1.0/3.0).abs() < 1e-10);
/// assert!((pr[1] - 1.0/3.0).abs() < 1e-10);
/// assert!((pr[2] - 1.0/3.0).abs() < 1e-10);
/// ```
pub fn pagerank(graph: &Graph) -> IgraphResult<Vec<f64>> {
let n = graph.vcount();
let n_us = n as usize;
if n == 0 {
return Ok(Vec::new());
}
if n == 1 {
return Ok(vec![1.0]);
}
let directed = graph.is_directed();
// Pre-compute per-vertex out-degree and in-neighbour adjacency:
// in_adj[v] = list of (u, 1/out_deg(u)) for each in-edge u → v.
// For undirected graphs we use the symmetric `neighbors()` iteration
// (each edge contributes both directions).
let n_f = f64::from(n);
let mut out_deg = vec![0u64; n_us];
if directed {
for v in 0..n {
let v_us = v as usize;
// Count out-edges of v: use Graph's pub(crate) helper via neighbors()
// (which returns out-only for directed).
let nbrs = graph.neighbors(v)?;
out_deg[v_us] = nbrs.len() as u64;
}
} else {
for v in 0..n {
let v_us = v as usize;
let nbrs = graph.neighbors(v)?;
// For undirected, neighbors() returns each incident edge once
// (LOOPS_TWICE for self-loops). The "out degree" for PageRank
// is the total degree.
out_deg[v_us] = nbrs.len() as u64;
}
}
// Build the in-adjacency: for each edge u → v (or u-v undirected, both
// u→v and v→u), append u to in_adj[v].
let mut in_adj: Vec<Vec<u32>> = vec![Vec::new(); n_us];
if directed {
// Iterate every edge once and record u → v.
let m = u32::try_from(graph.ecount())
.map_err(|_| crate::core::IgraphError::Internal("ecount overflows u32"))?;
for e in 0..m {
let (u, v) = graph.edge(e)?;
in_adj[v as usize].push(u);
}
} else {
// Undirected: each (u, v) edge appears once; record both directions.
let m = u32::try_from(graph.ecount())
.map_err(|_| crate::core::IgraphError::Internal("ecount overflows u32"))?;
for e in 0..m {
let (u, v) = graph.edge(e)?;
// Self-loop in undirected has degree 2 contribution so we add
// both directions.
if u == v {
in_adj[v as usize].push(u);
in_adj[v as usize].push(u);
} else {
in_adj[u as usize].push(v);
in_adj[v as usize].push(u);
}
}
}
// Initial uniform distribution.
let mut pr = vec![1.0 / n_f; n_us];
let mut pr_new = vec![0.0_f64; n_us];
for _ in 0..DEFAULT_MAX_ITER {
// Compute total dangling-vertex rank for redistribution.
let mut dangling_sum: f64 = 0.0;
for v in 0..n_us {
if out_deg[v] == 0 {
dangling_sum += pr[v];
}
}
let teleport = (1.0 - DEFAULT_DAMPING) / n_f;
let dangling_share = DEFAULT_DAMPING * dangling_sum / n_f;
for v in 0..n_us {
let mut incoming: f64 = 0.0;
for &u in &in_adj[v] {
#[allow(clippy::cast_precision_loss)]
let denom = out_deg[u as usize] as f64;
if denom > 0.0 {
incoming += pr[u as usize] / denom;
}
}
pr_new[v] = teleport + dangling_share + DEFAULT_DAMPING * incoming;
}
// Convergence: L1 norm of the change.
let mut diff: f64 = 0.0;
for v in 0..n_us {
diff += (pr_new[v] - pr[v]).abs();
}
std::mem::swap(&mut pr, &mut pr_new);
if diff < DEFAULT_EPS {
break;
}
}
Ok(pr)
}
#[cfg(test)]
mod tests {
use super::*;
fn close(actual: &[f64], expected: &[f64], tol: f64) {
assert_eq!(actual.len(), expected.len(), "length mismatch");
for (i, (a, e)) in actual.iter().zip(expected.iter()).enumerate() {
assert!((a - e).abs() < tol, "vertex {i}: actual={a} expected={e}");
}
}
#[test]
fn empty_graph_yields_empty() {
let g = Graph::with_vertices(0);
assert!(pagerank(&g).unwrap().is_empty());
}
#[test]
fn singleton_yields_one() {
let g = Graph::with_vertices(1);
assert_eq!(pagerank(&g).unwrap(), vec![1.0]);
}
#[test]
fn isolated_vertices_uniform() {
// No edges: all vertices are dangling. The dangling-redistribution
// term keeps the distribution uniform → 1/n each.
let g = Graph::with_vertices(4);
let pr = pagerank(&g).unwrap();
close(&pr, &[0.25, 0.25, 0.25, 0.25], 1e-9);
}
#[test]
fn triangle_uniform_one_third() {
let mut g = Graph::with_vertices(3);
g.add_edge(0, 1).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(2, 0).unwrap();
let pr = pagerank(&g).unwrap();
close(&pr, &[1.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0], 1e-9);
}
#[test]
fn directed_4cycle_uniform_quarter() {
let mut g = Graph::new(4, true).unwrap();
for i in 0..4u32 {
g.add_edge(i, (i + 1) % 4).unwrap();
}
let pr = pagerank(&g).unwrap();
close(&pr, &[0.25, 0.25, 0.25, 0.25], 1e-9);
}
#[test]
fn pagerank_sums_to_one() {
// K4 minus an edge — verify normalization.
let mut g = Graph::with_vertices(4);
g.add_edge(0, 1).unwrap();
g.add_edge(0, 2).unwrap();
g.add_edge(1, 2).unwrap();
g.add_edge(1, 3).unwrap();
g.add_edge(2, 3).unwrap();
let pr = pagerank(&g).unwrap();
let total: f64 = pr.iter().sum();
assert!((total - 1.0).abs() < 1e-9, "sum {total} != 1.0");
}
#[test]
fn star_centre_has_higher_pagerank_than_leaves() {
let mut g = Graph::with_vertices(4);
for v in 1..4 {
g.add_edge(0, v).unwrap();
}
let pr = pagerank(&g).unwrap();
// Centre receives from 3 leaves, each leaf only from centre → centre > leaf.
for &leaf in &pr[1..4] {
assert!(pr[0] > leaf, "centre {} not > leaf {}", pr[0], leaf);
}
// Symmetry among leaves.
close(&pr[1..4], &[pr[1], pr[1], pr[1]], 1e-9);
}
#[test]
fn pagerank_dangling_node_distributes() {
// Directed: 0 → 1, vertex 1 is dangling. Power iteration plus
// dangling-redistribution keeps PR finite and summing to 1.
let mut g = Graph::new(2, true).unwrap();
g.add_edge(0, 1).unwrap();
let pr = pagerank(&g).unwrap();
let total: f64 = pr.iter().sum();
assert!((total - 1.0).abs() < 1e-9);
// Vertex 1 receives flow from 0 and the dangling-redistribution.
// Vertex 0 only receives the teleport + dangling-redistribution.
// → pr[1] > pr[0].
assert!(pr[1] > pr[0]);
}
}