Graph Construction

Graph construction decides which nodes and edges a model sees. For molecular and protein modeling, it is often as important as the GNN architecture itself.

A radius graph connects nodes within a cutoff:

$$(i,j)\in E⟺\Vert x_i-x_j{\Vert }_2\le r$$

A k-nearest neighbor graph connects each node to its nearest neighbors:

$$\mathcal{N}(i)=\mathrm{kNN}(x_i;\{x_j{\}}_{j\ne i},k)$$

Common Choices

Graph Type	Nodes	Edges	Typical Use
Chemical bond graph	atoms	covalent bonds	molecular property prediction, graph pretraining
contact map	residues	distance/contact threshold	protein structure and function modeling
radius graph	atoms, residues, points	$\Vert x_i-x_j{\Vert }_2\le r$	local 3D message passing
k-nearest neighbor graph	atoms, residues, embeddings	nearest neighbors by distance or similarity	fixed-degree geometric models
bipartite interaction graph	protein nodes and ligand nodes	cross edges between sets	protein-ligand interaction, docking, scoring
fully connected graph	all nodes	all pairs	small molecules, attention-heavy graph transformers

Construction Function

Write graph construction as a function:

$$G=C_{\psi }(u,r,c)=(V,E,A)$$

where $u$ is the raw entity, $r$ is the representation, $c$ is context such as pocket or conformer protocol, and $A$ contains node, edge, or pair attributes. This makes clear whether graph construction is deterministic, learned, cached, or context-dependent.

Edge Attributes

Attribute	Meaning	Risk
bond type	chemical relation	aromaticity, charge, stereo, and hydrogens depend on standardization
distance	coordinate relation	coordinate source and unit must be fixed
direction vector	equivariant relation	frame and rotation behavior must be explicit
sequence separation	residue relation	chain breaks and missing residues matter
interaction type	protein-ligand relation	may be derived from known pose or post-hoc annotation
learned relation	model-discovered edge	can hide data leakage if fit using test data

Leakage Boundary

Graph construction can leak when edges use information unavailable at inference:

$$E_{\mathrm{eval}}⊈E_{\mathrm{inference}}\Rightarrow \text{claim mismatch}$$

Examples include ligand-defined pockets in blind docking, contact maps from target structures unavailable in deployment, similarity graphs built using the full benchmark, or conformer/pose edges generated after seeing labels.

Checks

• What is a node: atom, residue, conformer, pocket point, or abstract entity?
• Are edges chemical, spatial, sequential, learned, or task-specific?
• Does graph construction use target information or future data?
• Are cutoff and $k$ values stable across molecule and protein sizes?
• Is graph construction performed before or after the split?
• Are coordinates, conformers, pockets, and templates available at inference?
• Are node ordering, atom mapping, and residue indexing stable across preprocessing?

Related

• Graph neural networks
• Molecular graph
• Graph Transformer
• Equivariant GNN
• Representation contract
• Coordinate modeling contract