A new way to solve the graph classification problem is addressed. The main method utilized is the application of a capsule neural network on graphs. The results achieved include, firstly, the enhancement of the base algorithm for training a capsule network with the possibility of using graphs as an input (a stage of training for permutation invariants of graph vertices’ transformation matrices is included as well as a memory block for trained matrices), and secondly, a proposition of a training set of labeled graph objects, transformed from the MNIST dataset. This opens a perspective for a better classification of graph objects due to preserving of their structure and transformation invariance between layers.