Graphons: A Nonparametric Method to Model, Estimate, and Design Algorithms for Massive Networks

Abstract: Many social and economic systems are naturally represented as networks, from off-line and on-line social networks, to bipartite networks, like Netflix and Amazon, between consumers and products. Graphons, developed as limits of graphs, form a natural, nonparametric method to describe and estimate large networks like Facebook and LinkedIn. Here we describe the development of the theory of graphons, for both dense and sparse networks, over the last decade. We also review theorems showing that we can consistently estimate graphons from massive networks in a wide variety of models. Finally, we show how to use graphons to estimate missing links in a sparse network, which has applications from estimating social and information networks in development economics, to rigorously and efficiently doing collaborative filtering with applications to movie recommendations in Netflix and product suggestions in Amazon.