Function spectral_embedding 

pub fn spectral_embedding<N>(
    nodes: &[N],
    edges: &[(N, N, f32)],
    max_iterations: usize,
    tolerance: f64,
) -> Vec<(N, (f64, f64))>
where
    N: Clone + Ord,

Deterministic 2D spectral layout over an abstract undirected, unweighted graph. Returns one (node, (x, y)) pair per distinct node with both coordinates min–max normalised to [0, 1].

The coordinates are the two smallest non-trivial eigenvectors of the graph Laplacian L = D − A (the Fiedler vector and the next one) — the classic spectral-drawing layout: graph-adjacent nodes land near each other and disconnected components separate cleanly, so a client force-directed layout seeded from these hints converges faster and to a stable arrangement. The hint is purely advisory; callers may seed their own layout with it or ignore it entirely.

Method: shifted, deflated power iteration. We iterate on M = cI − L (whose DOMINANT eigenvectors are L’s SMALLEST), deflating the trivial constant mode (L-eigenvalue 0) and then each found coordinate via Gram–Schmidt, so successive sweeps recover the next Laplacian eigenvector. max_iterations caps the sweeps per coordinate; tolerance is the L1 convergence threshold on successive normalised iterates.

Determinism (guaranteed and tested): the node universe is a sorted, deduped BTreeSet; the start vectors are fixed index-polynomial seeds (no random initialisation); sweeps run in ascending index order with a fixed cap. The eigenvector sign — mathematically arbitrary — is pinned by the fixed seed, so identical input always produces identical coordinates. An isolated node or an edgeless / single-node graph still yields finite, deterministic hints (a degenerate coordinate collapses to 0.5).