formal definitions of transitivity.[]{data-label="fig:examples"}](exampleMultiGen.pdf)

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General framework
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Notation and basic concepts
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Let us start with introducing some notations. We assume that the data is structured as a graph $G = ({\mathcal{V}},{\mathcal{E}},{Q})$, where ${\mathcal{V}}$ corresponds to the set of nodes ${v}$ and ${\mathcal{E}}\subseteq {\mathcal{V}}^2$ represents the set of edges ${e}$, for which training labels are provided in terms of relations. Moreover, these relations are represented by training weights ${y}_{{e}}$ on the edges, generated from an unknown underlying relation ${Q}: {\mathcal{V}}^2 \rightarrow [0,1]$. Relations are required to take values in the interval $[0,1]$ because some properties that we need are historically defined for such relations, but an extension to real-graded relations ${h}: {\mathcal{V}}^2 \rightarrow {\mathbb{R}}$ can always be realized. Consider $b \in {\mathbb{R}}^+$ and an increasing isomorphism $\sigma : [-b,b] \rightarrow [0,1]$ that satisfies $\sigma(x) = 1 - \sigma(-x)$, then we consider the ${\mathbb{R}}\rightarrow [0,1]$ mapping $\nabla$ defined by: $$\begin{aligned}
\nabla(x) & = & \left\{ \begin{array}{ll} 0, &
\textrm{if $ x \le -b$}\\
\sigma(x), &  \textrm{if $-b \le x \le b$} \\
1, & \textrm{if $b \le x$}
\end{array} \right.\end{aligned}$$ and its inverse $\nabla^{-1} = \sigma^{-1}$.

Any real-valued relation ${h}: {\mathcal{V}}^2 \rightarrow {\mathbb{R}}$ can be transformed into a 