Network Models for Data Science Theory, Algorithms, and Applications

In this chapter, we discuss various issues that arise when networks increase in size. What does it mean for a network to increase in size and how would we visualize that process? Can a sequence of networks, increasing in size, converge to a limit, and what would such a limit look like? We discuss the transformation of an adjacency matrix to a pixel picture and what it means for a sequence of pixel pictures to increase in size. If a limit exists, the resulting function is called a limit graphon, but it is not itself a network. Estimation of a graphon is also discussed and methods described include an approximation by SBM and a network histogram.