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WeightedAdjacencyMatrix

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

WeightedAdjacencyMatrix[g]

gives the adjacency matrix of g with each entry the corresponding edge's weight (0 where there is no edge). Equal to AdjacencyMatrix[g] when g has no EdgeWeight.

Examples (6)

Every input below was run against the current Mathilda build and its output recorded.

Basic examples (2)

In[1]:= WeightedAdjacencyMatrix[CycleGraph[4]] == AdjacencyMatrix[CycleGraph[4]]
Out[1]= True

In[2]:= WeightedAdjacencyMatrix[5]
Out[2]= WeightedAdjacencyMatrix[5]

Options (2)

In[3]:= WeightedAdjacencyMatrix[Graph[{1,2,3},{1->2,2->3},EdgeWeight->{5,7}]]
Out[3]= {{0, 5, 0}, {0, 0, 7}, {0, 0, 0}}

In[4]:= WeightedAdjacencyMatrix[Graph[{1,2,3},{1<->2,2<->3},EdgeWeight->{5,7}]]
Out[4]= {{0, 5, 0}, {5, 0, 7}, {0, 7, 0}}

Applications (2)

Weights fill the adjacency cells

In[5]:= WeightedAdjacencyMatrix[Graph[{1, 2, 3}, {1 <-> 2, 2 <-> 3}, EdgeWeight -> {5, 7}]]
Out[5]= {{0, 5, 0}, {5, 0, 7}, {0, 7, 0}}

Unweighted: every present edge is 1

In[6]:= WeightedAdjacencyMatrix[CycleGraph[3]]
Out[6]= {{0, 1, 1}, {1, 0, 1}, {1, 1, 0}}

Algorithm

wtadjmat.c - WeightedAdjacencyMatrix[g]: dense adjacency matrix filled with per-edge weights instead of a literal 1.

Same algorithm as AdjacencyMatrix (adjmat.c): a DirectedEdge[a,b] sets M[a][b] = weight(a,b); an UndirectedEdge sets both M[a][b] and M[b][a]. Any entry with no edge is 0. For a graph with no EdgeWeight, every weight defaults to 1 (graph_resolve_edge_weights), so WeightedAdjacencyMatrix[g] == AdjacencyMatrix[g] exactly for an unweighted g.

Memory (SPEC section 4): returns a freshly-allocated matrix; frees res.

Implementation notes

Algorithm. builtin_weighted_adjacency_matrix builds the dense n x n adjacency matrix filled with per-edge weights instead of a literal 1. It is the same construction as AdjacencyMatrix: a DirectedEdge[a, b] sets M[a][b] = weight(a, b), an UndirectedEdge sets both M[a][b] and M[b][a], and any cell with no edge is 0. The weights come from graph_resolve_edge_weights, the shared resolver that returns g's EdgeWeight list or {1, ..., 1} when there is none ā€” so for an unweighted graph WeightedAdjacencyMatrix[g] equals AdjacencyMatrix[g] exactly.

Data structures. A flat n*n grid of Expr* cells, a GraphVIdx mapping each vertex to its row/column index, and the resolved weight list. The grid is assembled into a List of row Lists; empty cells become expr_new_integer(0).

Complexity / limits. O(n^2) to materialize the dense matrix plus O(E) to place the weights. Weights are copied verbatim, so symbolic weights appear as-is in the matrix. Returns NULL (unevaluated) for a non-graph argument.

  • Protected. Equal to AdjacencyMatrix[g] exactly when g has no EdgeWeight (every weight defaults to 1). Undirected edges put their weight in both symmetric positions.
  • Mathematica returns a SparseArray; Mathilda returns a dense matrix.
  • Unevaluated on a non-graph.

Attributes: Protected.

References

See also: EdgeWeight, SparseArray

Notes & additional examples

Notes

WeightedAdjacencyMatrix[g] is the dense adjacency matrix with each present edge's EdgeWeight in place of a 1; absent edges are 0. An undirected edge fills both symmetric cells, a directed edge only M[tail][head].

For a graph with no weights every edge defaults to weight 1, so the result coincides with AdjacencyMatrix[g]. The row and column order is VertexList order.