Given a certain haplotype pair H, the authors defined a graph G X (H) such that there is a vertex for each column of the matrix X and there is an edge between two vertices of G X (H) if the corresponding columns in X are linked by at least one fragment.
Now, consider a graph such that it has a vertex for each column of M corresponding to a heterozygous site and there is an edge between two vertices if the corresponding error matrix does not reveal inconsistencies (i.e. the matrix is diagonal and of full rank).
Before presenting this result, let us consider the adjacency matrix (here the first row and column correspond to vertex x n, the second row and column correspond to vertex x n − 1, … , etc). of Γ ( S M ) which is defined by its entries a i j = 1 if x i x j ∈ E ( Γ ( S M ) ) and 0 otherwise (see A ( Γ ( S M ) ) in Figure 3).
After folding, a graph is constructed using adjacency matrix F, where each column is a vertex and if the entry at the intersection between a row and a column is greater than zero then an edge is constructed between the corresponding vertices.
Specially, for (v in V(G)), let (L_{v}(G)) be the principal submatrix of (L(G)) formed by deleting the row and column corresponding to vertex v, then the eigenvalues of (L_{v}(G)) interlace the eigenvalues of (L(G)).
Each potential functional label of a node at index j of P, appears as a contextual-label vertex in the j-th column of the corresponding context-label network.
To assign unlabeled cases to classes, the data is entered into a large matrix (cases along rows and predictors along columns) that is augmented by vertex coordinates stored in the last c−1 columns.
Index this column by 0. Let vertex 0 be the parent of c i for all 1 ≤ i ≤ d.
Let u be a column of B and a vertex of (T,w).
Now, we label some vertices of T(A) as follows: If the last 1 entry in row r occurs in column j, then we label vertex j of T(A) with r.
