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When each data point is a large graph, graph statistics such as densities ofcertain subgraphs (motifs) can be used as feature vectors for machine learning.While intuitive, motif counts are expensive to compute and difficult to workwith theoretically. Via graphon theory, we give an explicit quantitative boundfor the ability of motif homomorphisms to distinguish large networks under bothgenerative and sampling noise. Furthermore, we give similar bounds for thegraph spectrum and connect it to homomorphism densities of cycles. This resultsin an easily computable classifier on graph data with theoretical performanceguarantee. Our method yields competitive results on classification tasks forthe autoimmune disease Lupus Erythematosus.

Classification on Large Networks: A Quantitative Bound via Motifs and Graphons