Probabilistic molecular graph models Let a collection of molecular graphs have at most $N$ nodes, $d$ node types (atom type), and $t$ edge types (bond types). A graph from this collection is normally represented by the tuple $(F, E)$ with

\begin{equation}
\text { node-label matrix } F \in \mathbb{R}^{N \times(1+d)}\quad \text { and }\quad \text{edge-label tensor } E \in \mathbb{R}^{N \times N \times(1+t)}
\end{equation}

In a statistical model, $i$-th row in matrix $F$ represents the probability of different node types for a node $v_i$. Similarly, filament $(i,j,:)$ of tensor $E$ represents the probabilities of edge $\epsilon_{i,j}$ in the graph. 

In these models, usually, probabilities of nodes and edges are assumed to be independent. This, however, is not a realistic assumption. Type of atoms and bonds are obviously not independent from each other. For a node of certain type, the incident edges collectively must have total type values not exceeding a threshold, where the “type value” is some numeric property of an edge type.

Question:

I was wondering if the type of the node is only dependent on its immediate neighboring edges (incident edges) or we can argue that it also is affected by the edges farther from the node.
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.