Two types of redundancy arise from linearly dependence. (a) A cycle c is decomposed into a tree path p2 and a path p1 that contains a non-tree edge e. So we have bc = bp + bt, where bc, bp, and bt are constraints of cycle c, path p1 and path p2, respectively. The dotted line represents the non-tree edge e. (b) nl is the node closest to ni on the path p3. Assume that the constraint of tree path pi is bi, 1 ≤ i ≤ 6. We have b1 = b4 + b6, b2 = b4 + b5, and b3 = b5 + b6, which conclude that b1 = b2 + b3 due to the addition over GF(2).
Lai et al. BMC Bioinformatics 2012 13(Suppl 17):S19 doi:10.1186/1471-2105-13-S17-S19