## 5 Tests and Results  
### Datasets Description  
The proposed comparison among different data granulation strategies involves 11 different datasets, with the first 6 datasets being taken from the IAM Repository [49] and the remaining ones being taken from the TUDataset Repository [50]. A brief description of the datasets, along with the formal definition of the dissimilarity measures between nodes and edges, follows:  
* The AIDS dataset consists of 2000 graphs representing molecules showing activity or not against HIV (two classes). Molecules are converted into graphs in a straightforward manner by representing atoms as nodes and the covalent bonds as edges. Nodes are labeled by a three-element tuple that collects the 2D \(\langle x,y\rangle\) coordinates of the atom, the chemical symbol (categorical) and its charge (integer). Although edges are originally labeled with the valence of the linkage, such a value has been discarded since it is not useful for the classification task. * The Letter-L dataset involves graphs that represent distorted letter drawings with a low level of distortion. The recognition task involves the 15 capital letters of the Roman alphabet that can be represented by straight lines only. Each handwritten letter is transformed into a graph by representing lines as edges and endpoints of lines as nodes. Each node is labeled by a two-dimensional real-valued vector giving its position within a reference coordinate system. Conversely, edges are unlabeled. * Same as Letter-L, but with medium level of distortion in handwritten digits. * Same as Letter-L, but with high level of distortion in handwritten digits. * The GREC dataset consists of symbols from electronic and architectural drawings and, after suitable pre-processing, graphs are extracted from such images. Ending points, corners, intersections and circles are represented by nodes and labeled with a two-dimensional attribute giving their position. The nodes are connected by undirected edges, which are labeled as \"line\" or \"arc\". An additional attribute specifies the \"angle\" with respect to the horizontal direction or the diameter in case of arcs. * The Mutagenicity dataset consists of 4337 graphs corresponding to chemical compounds divided into two classes, depending on their respective mutagenic propensity for being a marketable drug or not. Both nodes and edges are equipped with categorical labels: node labels identify the atom type and edge labels identify the valence of the linkage. * The MUTAG dataset consists of 188 graphs corresponding to chemical compounds divided into two classes according to their respective mutagenic effect on a bacterium. Both nodes and edges are equipped with categorical labels: node labels identify the atom type and edge labels identify the bond type (single, double, triple or aromatic). * The DD dataset (also known as D&D) contains 1178 protein structures. Each protein is represented by a graph, in which the nodes are amino-acids and two nodes are connected by an edge if they are less than 6A apart. Nodes encode a categorical label (i.e., the amino-acid type), whereas edges are unlabeled. The prediction task is to classify the protein structures into enzymes and non-enzymes. * Each graph is used as representation of a chemical compound: each vertex stands for an atom of the molecule, and edges between vertices represent bonds between atoms. This dataset is relative to anti-cancer screens, where the chemicals are assessed as positive or negative to cell lung cancer. Each vertex has a categorical label representing the corresponding atom type, whereas edges are unlabeled. * Each graph represents a simplified protein tertiary structure, where nodes correspond to secondary structure elements and edges connect nodes if those are neighbors along the primary structure (i.e., the amino-acid sequence) with the constraint that every node is connected to its three nearest spatial neighbors.