MIVIA Dataset of Biological Graphs

The databases have been structured for the monomorphism problem, so each one is composed of very large graphs, called target, from which have been extracted a set of not induced subgraphs, called pattern, and so grouped by three densities: 1, 0.5 and 0.25. The aim of the authors is to use pattern graphs as queries on the target graph. We do not use all the six databases, but the following tree:

• AIDS: a molecular database containing 40000 graphs, from 4 to 256 nodes, representing the topological structure of a chemical compound tested for evidence of anti-HIV activity. 
• Graemlin: database contains 10 target graphs having up to 6726 nodes, extracted from 10 microbial networks.
• Protein-Protein interaction (PPI): a dataset networks contains 10 network graphs, from 5720 to 12575 nodes, describing known protein interactions of 10 organisms. This is composed of more dense and big graphs than those in Graemlin.

The Graemlin and PPI databases have nodes with no labels. Since graph matching algorithms usually employ label information to reduce the computational costs, the matching times on unlabeled graphs are very long. For this reason, we have attached labels to the nodes of the graphs. The labels have been generated using random integer values. We have generated 5 labeled version of each database, varying the number of possible label values (128, 256, 512, 1024 and 2048 values have been used). For graph isomorphism we have generated two new databases, extracting random node-induced subgraphs from the target graphs in Graemlin and PPI; for each graph, 10 random permutations of the nodes have been computed to obtain isomorphic pairs of graphs. In order to test isomorphism algorithms on dense graphs, we have also added extra edges at random. So finally we have two isomorphism databases having 700 pairs, varying from 8 to 512 nodes.