Heterogeneous Graphs

Most GNN models consider graphs to be homogeneous - that is, all nodes being of one type, despite many possible instances of problems, where it would be beneficial to utilize information about entities’ types and their relations’ types. In PyNeuraLogic, we can easily encode instances of such heterogeneous graphs with an arbitrary number of nodes’ and edges’ classes out of the box.

Let’s consider the graph in the above figure, where nodes’ color represents their type (either Blue or Pink). We can represent introduced nodes’ types in the input examples, for example, as the following list of ground relations:

Relation.type(1, Term.BLUE),
Relation.type(2, Term.BLUE),
Relation.type(3, Term.PINK),
Relation.type(4, Term.PINK),
Relation.type(5, Term.PINK),

Note

Note that there are many ways to express the same concept. We could, for example, encode types (for nodes 1 and 3) as Relation.blue(1), Relation.pink(3). Nodes are also not limited to have only one type; we can assign multiple types to one node, such as Relation.type(1, Term.BLUE), Relation.type(1, Term.PINK).

Note

In this example, we consider only nodes’ types, but we can analogically encode edges’ (or any other) types.

We can then utilize the information about types for various use cases. In the following example, we showcase a template rule for the aggregation of neighbor nodes of the central node with the same type as the central node.

Relation.h(Var.X) <= (
    Relation.feature(Var.Y),
    Relation.type(Var.X, Var.Type),
    Relation.type(Var.Y, Var.Type),
    Relation.edge(Var.Y, Var.X),
)

Since types are just regular constructs (relations) in PyNeuraLogic, we are able to manipulate them as anything else. We can, for example, create hierarchies of types or, as is shown in the following example, attach features to types in input examples and then utilize them in the aggregation.

Relation.type_feature(Term.BLUE)[[1, 2, 3]]

Relation.h(Var.X) <= (
    Relation.feature(Var.Y),
    Relation.type_feature(Var.Type),
    Relation.type(Var.Y, Var.Type),
    Relation.edge(Var.Y, Var.X),
)