On the Rank, Kernel, and Core of Sparse Random Graphs

Patrick DeMichele, Margalit Glasgow, Alexander Moreira

We study the rank of the adjacency matrix $A$ of a random Erdos Renyi graph $G\sim \mathbb{G}(n,p)$. It is well known that when $p=(\log (n)-\omega (1))/n$, with high probability, $A$…