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. Author manuscript; available in PMC: 2012 Jun 1.
Published in final edited form as: Phys Biol. 2011 May 13;8(3):035012. doi: 10.1088/1478-3975/8/3/035012

Figure 2.

Figure 2

Matrix operations for the proof of invertibility of matrices. The gray area corresponds to P and the dark gray area corresponds to the submatrix spanned by nodes that are not sink nodes. The yellow and green areas are submatrices Q and R, respectively S is left blank. The n-th column/row are highlighted in Figure (a). (b) Matrix after summing up all rows/columns and putting the result in the n-th row/column. (c) Matrix after cleaning all, but the last element in the n-th row/column (d) Final matrix after removing all nonzero elements in the light gray area. The dark grey matrix remains non-zero.