Module bridge 

Graph <-> matrix conversions: adjacency (boolean, min-plus, sparse), incidence, and Laplacian, with explicit multiedge policies and a mapping witness.

Bridge matrices omit graph self-loops. This keeps adjacency, incidence, and Laplacian exports aligned with the simple-graph matrix contract while preserving the original graph value unchanged.

Structs

GraphMatrixMap

Mapping metadata recording how graph elements landed in the matrix.

Enums

MultiedgePolicy

How to collapse parallel edges between the same endpoints into one cell.

Functions

graph_to_bool_adjacency

Boolean adjacency: true where at least one non-self-loop edge connects the pair.

graph_to_incidence

Incidence matrix as a sparse IntRing matrix. Directed: -1 at the source, +1 at the target. Undirected: +1 at both endpoints. One column per non-self-loop edge.

graph_to_laplacian

Unweighted graph Laplacian L = D - A over IntRing, ignoring self-loops. For an undirected graph each row sums to zero.

graph_to_minplus_adjacency

Min-plus weighted adjacency (Inf = no non-self-loop edge), applying a multiedge policy.

graph_to_sparse_adjacency

Sparse min-plus weighted adjacency, applying a multiedge policy and omitting self-loops.

minplus_adjacency_to_graph

Reconstruct a graph from a min-plus adjacency matrix (Inf = no edge). Node labels are their indices. Directedness is supplied by the caller.