Theorems · Definition · combinatorics
SimpleGraph.adjMatrix
(α : Type u_1) → {V : Type u_2} → (G : SimpleGraph V) → [DecidableRel G.Adj] → [Zero α] → [One α] → Matrix V V αadjMatrix G α is the matrix A such that A i j = (1 : α) if i and j are
adjacent in the simple graph G, and otherwise A i j = 0.
- Cited by
- 48 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses Quot.sound
- Assumes
- DecidableRelZeroOne
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Matrixstatement · cited by 4,303
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Matrix.ofproof · cited by 336
Cited by49
Results whose statement or proof uses this declaration.
- SimpleGraph.lapMatrixproof · cited by 16
- SimpleGraph.diagonal_hadamard_adjMatrixstatement and proof · cited by 4
- SimpleGraph.adjMatrix_hadamard_diagonalstatement and proof · cited by 4
- SimpleGraph.adjMatrix_mulVec_applystatement and proof · cited by 4
- SimpleGraph.isAdjMatrix_adjMatrixstatement · cited by 2
- SimpleGraph.compl_adjMatrix_completeGraphstatement · cited by 2
- SimpleGraph.lapMatrix_toLinearMap₂'proof · cited by 2
- SimpleGraph.transpose_adjMatrixstatement · cited by 2
- SimpleGraph.isSymm_adjMatrixstatement · cited by 1
- SimpleGraph.one_add_adjMatrix_add_compl_adjMatrix_eq_of_onestatement and proof · cited by 1
- SimpleGraph.lapMatrix_mulVec_applyproof · cited by 1
- SimpleGraph.compl_adjMatrix_eq_adjMatrix_complstatement and proof · cited by 1