  In colored graphs, node classes are often associated with either their
neighbors class or with information not incorporated in the graph associated
with each node. We here propose that node classes are also associated with
topological features of the nodes. We use this association to improve Graph
machine learning in general and specifically, Graph Convolutional Networks
(GCN).
  First, we show that even in the absence of any external information on nodes,
a good accuracy can be obtained on the prediction of the node class using
either topological features, or using the neighbors class as an input to a GCN.
This accuracy is slightly less than the one that can be obtained using content
based GCN.
  Secondly, we show that explicitly adding the topology as an input to the GCN
does not improve the accuracy when combined with external information on nodes.
However, adding an additional adjacency matrix with edges between distant nodes
with similar topology to the GCN does significantly improve its accuracy,
leading to results better than all state of the art methods in multiple
datasets.
