Title: 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.