Struct MotifTensor 

pub struct MotifTensor {
    pub data: Array3<f64>,
    pub n: usize,
}

A third-order motif tensor T[i,j,k] encoding 3-node interaction patterns.

For an undirected graph, entry T[i,j,k] = 1 iff the induced subgraph on {i,j,k} forms a triangle (all three edges present).

For directed/weighted variants, use directed_motif_tensor.

Fields

data: Array3<f64>

Shape: (n, n, n) where n = number of nodes

n: usize

Number of nodes

Implementations

impl MotifTensor

pub fn from_adjacency(adj: &Array2<f64>) -> Self

Build the triangle motif tensor from a graph adjacency matrix.

T[i,j,k] = A[i,j] * A[j,k] * A[i,k] (all three edges present).

For a 0/1 adjacency matrix this is exactly 1 for triangles and 0 otherwise. For weighted graphs the entry equals the product of the three edge weights.

Arguments

• adj – symmetric adjacency matrix (shape n × n)

pub fn triangle_count(&self) -> f64

Count the total number of directed triangles encoded in the tensor.

Each undirected triangle {i,j,k} contributes 6 directed entries (all permutations), so divide by 6 to get the undirected count.

pub fn tensor_vec_product(&self, x: &[f64]) -> Vec<f64>

Compute the tensor-vector product T ×_1 x ×_2 x:

(T x^2)[i] = Σ_{j,k} T[i,j,k] x[j] x[k]

This is the “mode-1 multilinear product” used in tensor eigenvector centrality.

pub fn z_eigenvector_centrality(&self) -> Result<(f64, Vec<f64>)>

Compute the Z-eigenvector centrality of the motif tensor using the shifted power method.

Returns (eigenvalue, eigenvector) where the eigenvector satisfies T x^2 = λ x. All entries of the returned vector are non-negative.

Errors

Returns GraphError::InvalidGraph if n = 0.