The Rank of Random Graphs
Abstract
We show that almost surely the rank of the adjacency matrix of the Erd\"os-R\'enyi random graph G(n,p) equals the number of non-isolated vertices for any c n/n<p<1/2, where c is an arbitrary positive constant larger than 1/2. In particular, the giant component (a.s.) has full rank in this range.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.