cphase (vertex a, vertex b):
    if ngbh a\{b} =/= {}:
        remove VOP (a, b)
    end if
    if ngbh b\{a} =/= {}:
        remove VOP (b, a)
    end if
    [It may happen that the condition in line 2 has not been fulfilled then, but is now due to the effect of line 5. So we check again:]
    if ngbh a\{b} =/= {}:
        remove VOP (a, b)
    end if
    [Now we can be sure that the the condition (ngbh c\{a, b} = {} or VOP[c] ∈ Z) is fulfilled for c = a, b and we may use the lookup table (cf.  Eq. (9)).]
    if {a, b} ∈ E :
        edge ← true
    else:
        edge ← false
    end if
    (edge, VOP[a], VOP[b]) ← cphase_table[edge, VOP[a], VOP[b]]


remove_VOP (vertex a, vertex b):
    [This reduces VOP[a] to I, avoiding (if possible) to use b as swapping partner.]
    [First, we choose a swapping partner c.]
    if ngbh a\{b} = {}:
        c ← any element of ngbh a\{b}
    else:
        c←b
    end if
    d ← decomposition lookup table [a]
    [c contains now a decomposition such as Eq. (7)]
    for v from last factor of d to first factor of d
        if v = −iX:
            local complementation (a)
        else: ( this means that v = iZ)
            local complementation (b)
    end if
    [Now, VOP[a] = I.]


local complementation (vertex a)
    [performs the operation specified in Definition 4]
    nv ← ngbh v
    for i ∈ nv :
        for j ∈ nv :
            if i < j:
                if (i, j) ∈ E:
                    remove edge (i, j)
                else:
                    add edge (i, j)
                end if
            end if
        end for
        VOP[i] ← VOP[i]sqrt(−iZ)
    VOP[v] ← VOP[v]sqrt(iX)
    end for