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Graph Matrices
James Dillon edited this page Jun 12, 2017
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A molecule is a chemical graph comprised of nodes (atoms) and edges (bonds) that can be represented numerically in matrix format. Functions to compute the graph matrices of a molecule are provided by the Molecules.topology.matrix module.
The adjacency matrix (Molecules.topology.matrix.adjacency) is a square matrix of a hydrogen suppressed graph indicating pairs of adjacent atoms as 1 and non-adjacent atoms as 0.
var molecule = Molecules.load.smiles('CC(O)(C)C');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
// C1 C2 O3 C4 C5
// C1 [ 0, 1, 0, 0, 0 ]
// C2 [ 1, 0, 1, 1, 1 ]
// O3 [ 0, 1, 0, 0, 0 ]
// C4 [ 0, 1, 0, 0, 0 ]
// C5 [ 0, 1, 0, 0, 0 ]var molecule = Molecules.load.smiles('c1ccccc1');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
// c1 c2 c3 c4 c5 c6
// c1 [ 0, 1, 0, 0, 0, 1 ]
// c2 [ 1, 0, 1, 0, 0, 0 ]
// c3 [ 0, 1, 0, 1, 0, 0 ]
// c4 [ 0, 0, 1, 0, 1, 0 ]
// c5 [ 0, 0, 0, 1, 0, 1 ]
// c6 [ 1, 0, 0, 0, 1, 0 ]var molecule = Molecules.load.smiles('NC(C)C(O)=O');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
// N1 C2 C3 C4 O5 O6
// N1 [ 0, 1, 0, 0, 0, 0 ]
// C2 [ 1, 0, 1, 1, 0, 0 ]
// C3 [ 0, 1, 0, 0, 0, 0 ]
// C4 [ 0, 1, 0, 0, 1, 1 ]
// O5 [ 0, 0, 0, 1, 0, 0 ]
// O6 [ 0, 0, 0, 1, 0, 0 ]The degree matrix (Molecules.topology.matrix.degree) is a square matrix of a hydrogen suppressed graph that describes the total number of bonds of each atom along the matrix diagonal. The degree matrix is computed from the adjacency matrix of a chemical graph.
var molecule = Molecules.load.smiles('CC(O)(C)C');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
var degreeMatrix = Molecules.topology.matrix.degree(adjacencyMatrix);
// C1 C2 O3 C4 C5
// C1 [ 1, 0, 0, 0, 0 ]
// C2 [ 0, 4, 0, 0, 0 ]
// O3 [ 0, 0, 1, 0, 0 ]
// C4 [ 0, 0, 0, 1, 0 ]
// C5 [ 0, 0, 0, 0, 1 ]var molecule = Molecules.load.smiles('c1ccccc1');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
var degreeMatrix = Molecules.topology.matrix.degree(molecule);
// c1 c2 c3 c4 c5 c6
// c1 [ 2, 0, 0, 0, 0, 0 ]
// c2 [ 0, 2, 0, 0, 0, 0 ]
// c3 [ 0, 0, 2, 0, 0, 0 ]
// c4 [ 0, 0, 0, 2, 0, 0 ]
// c5 [ 0, 0, 0, 0, 2, 0 ]
// c6 [ 0, 0, 0, 0, 0, 2 ]var molecule = Molecules.load.smiles('NC(C)C(O)=O');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
var degreeMatrix = Molecules.topology.matrix.degree(molecule);
// N1 C2 C3 C4 O5 O6
// N1 [ 1, 0, 0, 0, 0, 0 ]
// C2 [ 0, 3, 0, 0, 0, 0 ]
// C3 [ 0, 0, 1, 0, 0, 0 ]
// C4 [ 0, 0, 0, 3, 0, 0 ]
// O5 [ 0, 0, 0, 0, 1, 0 ]
// O6 [ 0, 0, 0, 0, 0, 1 ]The distance matrix (Molecules.topology.matrix.distance) is a square matrix of a hydrogen suppressed graph that describes the minimum number of bonds (distance), that separate a pair of atoms. The distance matrix is computed from the adjacency matrix of a chemical graph.
var molecule = Molecules.load.smiles('CC(O)(C)C');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
var distanceMatrix = Molecules.topology.matrix.distance(adjacencyMatrix);
// C1 C2 O3 C4 C5
// C1 [ 0, 1, 2, 2, 2 ]
// C2 [ 1, 0, 1, 1, 1 ]
// O3 [ 2, 1, 0, 2, 2 ]
// C4 [ 2, 1, 2, 0, 2 ]
// C5 [ 2, 1, 2, 2, 0 ]var molecule = Molecules.load.smiles('c1ccccc1');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
var distanceMatrix = Molecules.topology.matrix.distance(adjacencyMatrix);
// c1 c2 c3 c4 c5 c6
// c1 [ 0, 1, 2, 3, 2, 1 ]
// c2 [ 1, 0, 1, 2, 3, 2 ]
// c3 [ 2, 1, 0, 1, 2, 3 ]
// c4 [ 3, 2, 1, 0, 1, 2 ]
// c5 [ 2, 3, 2, 1, 0, 1 ]
// c6 [ 1, 2, 3, 2, 1, 0 ]var molecule = Molecules.load.smiles('NC(C)C(O)=O');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
var distanceMatrix = Molecules.topology.matrix.distance(adjacencyMatrix);
// N1 C2 C3 C4 O5 O6
// N1 [ 0, 1, 2, 2, 3, 3 ]
// C2 [ 1, 0, 1, 1, 2, 2 ]
// C3 [ 2, 1, 0, 2, 3, 3 ]
// C4 [ 2, 1, 2, 0, 1, 1 ]
// O5 [ 3, 2, 3, 1, 0, 2 ]
// O6 [ 3, 2, 3, 1, 2, 0 ]The Laplacian matrix (Molecules.topology.matrix.laplacian) is a square matrix of a hydrogen suppressed graph. The Laplacian matrix is computed from the adjacency matrix and degree matrix of a chemical graph.
var molecule = Molecules.load.smiles('CC(O)(C)C');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
var degreeMatrix = Molecules.topology.matrix.degree(adjacencyMatrix);
var laplacianMatrix = Molecules.topology.matrix.laplacian(adjacencyMatrix, degreeMatrix);
// C1 C2 O3 C4 C5
// C1 [ 1, -1, 0, 0, 0 ]
// C2 [ -1, 4, -1, -1, -1 ]
// O3 [ 0, -1, 1, 0, 0 ]
// C4 [ 0, -1, 0, 1, 0 ]
// C5 [ 0, -1, 0, 0, 1 ]var molecule = Molecules.load.smiles('c1ccccc1');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
var degreeMatrix = Molecules.topology.matrix.degree(adjacencyMatrix);
var laplacianMatrix = Molecules.topology.matrix.laplacian(adjacencyMatrix, degreeMatrix);
// c1 c2 c3 c4 c5 c6
// c1 [ 2, -1, 0, 0, 0, -1 ]
// c2 [ -1, 2, -1, 0, 0, 0 ]
// c3 [ 0, -1, 2, -1, 0, 0 ]
// c4 [ 0, 0, -1, 2, -1, 0 ]
// c5 [ 0, 0, 0, -1, 2, -1 ]
// c6 [ -1, 0, 0, 0, -1, 2 ]var molecule = Molecules.load.smiles('NC(C)C(O)=O');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
var degreeMatrix = Molecules.topology.matrix.degree(adjacencyMatrix);
var laplacianMatrix = Molecules.topology.matrix.laplacian(adjacencyMatrix, degreeMatrix);
// N1 C2 C3 C4 O5 O6
// N1 [ 1, -1, 0, 0, 0, 0 ]
// C2 [ -1, 3, -1, -1, 0, 0 ]
// C3 [ 0, -1, 1, 0, 0, 0 ]
// C4 [ 0, -1, 0, 3, -1, -1 ]
// O5 [ 0, 0, 0, -1, 1, 0 ]
// O6 [ 0, 0, 0, -1, 0, 1 ]The Randic matrix (Molecules.topology.matrix.randic) is a square matrix of a hydrogen suppressed graph. The Randic matrix is computed from the adjacency matrix and degree matrix of a chemical graph.
var molecule = Molecules.load.smiles('CC(O)(C)C');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
var degreeMatrix = Molecules.topology.matrix.degree(adjacencyMatrix);
var randicMatrix = Molecules.topology.matrix.randic(adjacencyMatrix, degreeMatrix);
// C1 C2 O3 C4 C5
// C1 [ 0.0, 0.5, 0.0, 0.0, 0.0 ]
// C2 [ 0.5, 0.0, 0.5, 0.5, 0.5 ]
// O3 [ 0.0, 0.5, 0.0, 0.0, 0.0 ]
// C4 [ 0.0, 0.5, 0.0, 0.0, 0.0 ]
// C5 [ 0.0, 0.5, 0.0, 0.0, 0.0 ]var molecule = Molecules.load.smiles('c1ccccc1');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
var degreeMatrix = Molecules.topology.matrix.degree(adjacencyMatrix);
var randicMatrix = Molecules.topology.matrix.randic(adjacencyMatrix, degreeMatrix);
// c1 c2 c3 c4 c5 c6
// c1 [ 0.0, 0.5, 0.0, 0.0, 0.0, 0.5 ]
// c2 [ 0.5, 0.0, 0.5, 0.0, 0.0, 0.0 ]
// c3 [ 0.0, 0.5, 0.0, 0.5, 0.0, 0.0 ]
// c4 [ 0.0, 0.0, 0.5, 0.0, 0.5, 0.0 ]
// c5 [ 0.0, 0.0, 0.0, 0.5, 0.0, 0.5 ]
// c6 [ 0.5, 0.0, 0.0, 0.0, 0.5, 0.0 ]var molecule = Molecules.load.smiles('NC(C)C(O)=O');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
var degreeMatrix = Molecules.topology.matrix.degree(adjacencyMatrix);
var randicMatrix = Molecules.topology.matrix.randic(adjacencyMatrix, degreeMatrix);
// N1 C2 C3 C4 O5 O6
// N1 [ 0.00, 0.57, 0.00, 0.00, 0.00, 0.00 ]
// C2 [ 0.57, 0.00, 0.57, 0.33, 0.00, 0.00 ]
// C3 [ 0.00, 0.57, 0.00, 0.00, 0.00, 0.00 ]
// C4 [ 0.00, 0.33, 0.00, 0.00, 0.57, 0.57 ]
// O5 [ 0.00, 0.00, 0.00, 0.57, 0.00, 0.00 ]
// O6 [ 0.00, 0.00, 0.00, 0.57, 0.00, 0.00 ]The reciprocal matrix (Molecules.topology.matrix.reciprocal) is a square matrix of a hydrogen suppressed graph. The reciprocal matrix is computed from the distance matrix of a chemical graph.
var molecule = Molecules.load.smiles('CC(O)(C)C');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
var distanceMatrix = Molecules.topology.matrix.distance(adjacencyMatrix);
var reciprocalMatrix = Molecules.topology.matrix.reciprocal(distanceMatrix);
// C1 C2 O3 C4 C5
// C1 [ 0.0, 1.0, 0.5, 0.5, 0.5 ]
// C2 [ 1.0, 0.0, 1.0, 1.0, 1.0 ]
// O3 [ 0.5, 1.0, 0.0, 0.5, 0.5 ]
// C4 [ 0.5, 1.0, 0.5, 0.0, 0.5 ]
// C5 [ 0.5, 1.0, 0.5, 0.5, 0.0 ]var molecule = Molecules.load.smiles('c1ccccc1');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
var distanceMatrix = Molecules.topology.matrix.distance(adjacencyMatrix);
var reciprocalMatrix = Molecules.topology.matrix.reciprocal(distanceMatrix);
// c1 c2 c3 c4 c5 c6
// c1 [ 0.00, 1.00, 0.50, 0.33, 0.50, 1.00 ]
// c2 [ 1.00, 0.00, 1.00, 0.50, 0.33, 0.50 ]
// c3 [ 0.50, 1.00, 0.00, 1.00, 0.50, 0.33 ]
// c4 [ 0.33, 0.50, 1.00, 0.00, 1.00, 0.50 ]
// c5 [ 0.50, 0.33, 0.50, 1.00, 0.00, 1.00 ]
// c6 [ 1.00, 0.50, 0.33, 0.50, 1.00, 0.00 ]var molecule = Molecules.load.smiles('NC(C)C(O)=O');
var adjacencyMatrix = Molecules.topology.matrix.adjacency(molecule);
var distanceMatrix = Molecules.topology.matrix.distance(adjacencyMatrix);
var reciprocalMatrix = Molecules.topology.matrix.reciprocal(distanceMatrix);
// N1 C2 C3 C4 O5 O6
// N1 [ 0.00, 1.00, 0.50, 0.50, 0.33, 0.33 ]
// C2 [ 1.00, 0.00, 1.00, 1.00, 0.50, 0.50 ]
// C3 [ 0.50, 1.00, 0.00, 0.50, 0.33, 0.33 ]
// C4 [ 0.50, 1.00, 0.50, 0.00, 1.00, 1.00 ]
// O5 [ 0.33, 0.50, 0.33, 1.00, 0.00, 0.50 ]
// O6 [ 0.33, 0.50, 0.33, 1.00, 0.50, 0.00 ]