$[0,1]$-valued relation $Q$ as follows: $$\begin{aligned}
\label{eq:monmap}
Q({v},{v}') = \nabla(h({v},{v}')) \,, \quad \forall ({v},{v}') \in {\mathcal{V}}^2 \,,\end{aligned}$$ and conversely by means of $\nabla^{-1}$. In what follows we tacitly assume that $\nabla$ has been fixed.

Following the standard notations for kernel methods, we formulate our learning problem as the selection of a suitable function ${h}\in{\mathcal{H}}$, with ${\mathcal{H}}$ a certain hypothesis space, in particular a reproducing kernel Hilbert space (RKHS). More specifically, the RKHS supports in our case hypotheses $h: {\mathcal{V}}^2 \rightarrow {\mathbb{R}}$ denoted as $$\begin{aligned}
\label{eq:primalmodel}
h({e}) =  {\mathbf{w}}^T \Phi({e}) \,,\end{aligned}$$ with ${\mathbf{w}}$ a vector of parameters that needs to be estimated from training data, $\Phi$ a joint feature mapping for edges in the graph (see below) and ${\mathbf{a}}^T$ the transpose of a vector ${\mathbf{a}}$. Let us denote a training dataset of cardinality ${q}= |{\mathcal{E}}|$ as a set $T = \{({e},{y}_{{e}}) \mid {e}\in {\mathcal{E}}\}$ of input-label pairs, then we formally consider the following optimization problem, in which we select an appropriate hypothesis ${h}$ from ${\mathcal{H}}$ for training data $T$: $$\begin{aligned}
\label{regalgorithm}
\hat{{h}}=\operatorname*{argmin}_{{h}\in{\mathcal{H}}} \frac{1}{q} \sum_{{e}\in {\mathcal{E}}} {\mathcal{L}}({h}({e}),{y}_{{e}})
+{\lambda}\Arrowvert {h}\Arrowvert_{{\mathcal{H}}}^2 \,\end{aligned}$$ with ${\mathcal{L}}$ a given loss function, $\Arrowvert \cdot \Arrowvert_{{\mathcal{H}}}^2$ the traditional quadratic regularizer on the RKHS and ${\lambda}>0$ a regularization parameter. According 