Neural network for processing graph data

Methods, systems, and apparatus, including computer programs encoded on computer storage media, for receiving graph data representing an input graph comprising a plurality of vertices connected by edges; generating, from the graph data, vertex input data representing characteristics of each vertex in the input graph and pair input data representing characteristics of pairs of vertices in the input graph; and generating order-invariant features of the input graph using a neural network, wherein the neural network comprises: a first subnetwork configured to generate a first alternative representation of the vertex input data and a first alternative representation of the pair input data from the vertex input data and the pair input data; and a combining layer configured to receive an input alternative representation and to process the input alternative representation to generate the order-invariant features.