  Neural networks have been shown to be an effective tool for learning
algorithms over graph-structured data. However, graph representation
techniques---that convert graphs to real-valued vectors for use with neural
networks---are still in their infancy. Recent works have proposed several
approaches (e.g., graph convolutional networks), but these methods have
difficulty scaling and generalizing to graphs with different sizes and shapes.
We present Graph2Seq, a new technique that represents vertices of graphs as
infinite time-series. By not limiting the representation to a fixed dimension,
Graph2Seq scales naturally to graphs of arbitrary sizes and shapes. Graph2Seq
is also reversible, allowing full recovery of the graph structure from the
sequences. By analyzing a formal computational model for graph representation,
we show that an unbounded sequence is necessary for scalability. Our
experimental results with Graph2Seq show strong generalization and new
state-of-the-art performance on a variety of graph combinatorial optimization
problems.
