Function hub_and_authority_scores 

pub fn hub_and_authority_scores(graph: &Graph) -> IgraphResult<HitsScores>

Compute Kleinberg’s hub and authority scores.

Returns Ok(HitsScores) containing both vectors and the dominant eigenvalue of A·Aᵀ. The empty graph yields empty vectors and a 0.0 eigenvalue.

On undirected graphs the routine delegates to eigenvector_centrality, so hub == authority exactly and the reported eigenvalue is λ² (the square of the dominant adjacency-matrix eigenvalue).

Counterpart of igraph_hub_and_authority_scores(g, h, a, &val, /*weights=*/NULL, /*options=*/NULL) from references/igraph/src/centrality/hub_authority.c.

Examples

Pure hub / authority partition on a bipartite directed graph:

use rust_igraph::{Graph, hub_and_authority_scores};

// 0,1 → 2,3 — vertices 0,1 are pure hubs, 2,3 pure authorities.
let mut g = Graph::new(4, true).unwrap();
g.add_edges(vec![(0u32, 2u32), (0, 3), (1, 2), (1, 3)]).unwrap();
let s = hub_and_authority_scores(&g).unwrap();
assert!((s.hub[0] - 1.0).abs() < 1e-9);
assert!((s.hub[1] - 1.0).abs() < 1e-9);
assert!(s.hub[2].abs() < 1e-9);
assert!(s.hub[3].abs() < 1e-9);
assert!((s.authority[2] - 1.0).abs() < 1e-9);
assert!((s.authority[3] - 1.0).abs() < 1e-9);
// Largest eigenvalue of A·Aᵀ for this 2x2 hub-authority block is 4.
assert!((s.eigenvalue - 4.0).abs() < 1e-6);

Cross-relation invariant h ∝ A·a after convergence:

use rust_igraph::{Graph, hub_and_authority_scores};

let mut g = Graph::new(5, true).unwrap();
g.add_edges(vec![(0u32, 1u32), (0, 3), (1, 2), (1, 3), (2, 0), (2, 4), (3, 2), (4, 0), (4, 1)])
    .unwrap();
let s = hub_and_authority_scores(&g).unwrap();

// Compute A·authority by walking the edge list, then verify it lines
// up with hub after max-norming.
let n = g.vcount() as usize;
let mut a_auth = vec![0.0_f64; n];
for e in 0..g.ecount() {
    let (u, v) = g.edge(e as u32).unwrap();
    a_auth[u as usize] += s.authority[v as usize];
}
let max = a_auth.iter().fold(0.0_f64, |acc, &x| acc.max(x.abs()));
for x in &mut a_auth {
    *x /= max;
}
for u in 0..n {
    assert!((a_auth[u] - s.hub[u]).abs() < 1e-6);
}