I am reading "Social and Economic Networks" by M.Jackson. It is about random graphs. On Chapter 4, it says
[...] the degrees of two neighbors [i.e. neighboring nodes in a graph] are approximately independently distributed for large networks [i.e. graphs] provided the largest nodes are not too large.
What does "the largest nodes are not too large?" In particular, what does a large node mean? Does it mean a node with a high number of neighbors?