Function hub_and_authority_scores_weighted 

pub fn hub_and_authority_scores_weighted(
    graph: &Graph,
    weights: &[f64],
) -> IgraphResult<HitsScores>

Weighted Kleinberg hub and authority scores.

weights[e] is the weight of edge id e; must have length graph.ecount() or this returns IgraphError::InvalidArgument. The weighted adjacency matrix is W[i,j] = Σ_{e: i→j} w_e; the returned hub/authority vectors approximate the principal eigenvectors of W·Wᵀ and Wᵀ·W respectively.

Behaviour mirrors upstream igraph_hub_and_authority_scores when weights is non-NULL:

• Length must match ecount().
• All-zero weights → both vectors filled with 1.0, eigenvalue 0.
• Empty edges → same as the unweighted empty case.
• Negative weights are accepted: the sign-cleanup pass that normally zeros tiny negative drifts is skipped, since Perron-Frobenius no longer guarantees a non-negative eigenvector.
• Undirected graphs delegate to a self-rolled shifted power iteration on (W + I), and the reported eigenvalue is λ² (square of the dominant adjacency eigenvalue).

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

Examples

Weighted 2×2 bipartite block where weights tilt the authority:

use rust_igraph::{Graph, hub_and_authority_scores_weighted};

// 0→2 (w=1), 0→3 (w=4), 1→2 (w=2), 1→3 (w=3).
let mut g = Graph::new(4, true).unwrap();
g.add_edges(vec![(0u32, 2u32), (0, 3), (1, 2), (1, 3)]).unwrap();
let weights = vec![1.0, 4.0, 2.0, 3.0];
let s = hub_and_authority_scores_weighted(&g, &weights).unwrap();
// Both vertex 0 and 1 are hubs; vertex 2,3 are authorities.
assert!(s.hub[2].abs() < 1e-9);
assert!(s.hub[3].abs() < 1e-9);
assert!(s.authority[0].abs() < 1e-9);
assert!(s.authority[1].abs() < 1e-9);
// Authority 3 has heavier in-weight than authority 2.
assert!(s.authority[3] > s.authority[2]);