{\mathcal{G}}$, otherwise 0. Similarly, let $w(e)$ be the weight of the edge $e$, if $e \in {\mathcal{G}}$, otherwise 0. Also, let $N$ be the dimensionality of the vector space model defined by ${\mathcal{E}}$, such that ${\mathcal{V}}\in {\rm I\!R}^N$. ${\mathcal{E}}_V$ derives ${\mathcal{V}}$ from the vertices of ${\mathcal{G}}$. There is one vector attribute relative to each response object, therefore $N=|{\mathbb{G}}|$. ${\mathcal{V}}$ is derived from ${\mathcal{G}}$ such that $|{\mathcal{V}}|=N$, ${\mathcal{V}}[i]$ is the importance value of the $i$-th attribute, and ${\mathcal{V}}[i]=w(v_i)$. Despite the vector space increases linearly to the collection size, the resulting fusion vectors are mainly sparse, i.e., composed of few non-zero entries, which makes this embedding formulation simple and efficient in practice.

${\mathcal{E}}_H$ is a hybrid embedding approach based on both vertex and edge analysis. ${\mathcal{E}}_H$ encodes more information into the vector space, at a cost of a higher dimensionality.

The third approach, ${\mathcal{E}}_K$, extends the archetype to embed graphs as a histogram of kernels, where the vectorial attributes are selected by unsupervised selection of common subgraph patterns. The kernels are obtained from the centroids of a graph clustering process. Then, a vector quantization process, consisting of assignment and pooling procedures, is adopted to embed an input graph to the vector space. 