Probabilistic molecular graph models
Assuming that "atom type" already accounts for the actual nuclei and only refers to the different chemical character, I can think of examples of influence from a distance. 


The one with the smallest distance is the acidity of hydrogen attached to carbon. When we compare the hydrogens compared to the central carbon in Propane and Propionaldehyde, we observe a large difference.
Comparing any carbon of Benzene with one of the inner carbons of Butadiene, we observe a large difference in reactivity towards electrophiles.
The same comparison for a carbon of Benzene and the carbon in the 4 position of Pyridine yields a drop in nucleophilicity for the latter.