Algorithm 1

Begin

Set a significance level ∇min and a minimal Umin

For nodei, i ∈ [0, νmax − 1] and nodej, j ∈ [i + 1, νmax]

(Note: νmax is the total number of nodes)

For all empirical case samples N, compute a contingency table:

$${\mathrm{M}}_{\mathrm{ij}}=\begin{array}{cc}{N}_{11}& N_{12}\\ N_{21}& N_{22}\end{array}$$

For each relation type k out of the six cases find the solution:

Max Up

Subject to     Max Up > Umin

∇p > ∇min

∇error cells > ∇non-error cells

If the solution exists, then return a type k relation

End