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An m × n matrix: the m rows are horizontal and the n columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts.For example, a 2,1 represents the element at the second row and first column of the matrix.
Given a simple graph with vertices , …,, its Laplacian matrix is defined element-wise as [1],:= { = , or equivalently by the matrix =, where D is the degree matrix, and A is the graph's adjacency matrix.