A non-regular primitive permutation group is called extremely primitive if a point stabilizer acts primitively on each of its nontrivial orbits. Let $𝒮$ be a nontrivial finite regular linear space and $G\le \mathrm{Aut}\left(𝒮\right).$ Suppose that $G$ is extremely primitive on points and let rank$\left(G\right)$ be the rank of $G$ on points. We prove that rank$\left(G\right)\ge 4$ with few exceptions. Moreover, we show that $\mathrm{Soc}\left(G\right)$ is neither a sporadic group nor an alternating group, and $G=\mathrm{PSL}(2,q)$ with $q+1$ a Fermat prime if $\mathrm{Soc}\left(G\right)$ is a finite classical simple group.

A digraph in which any two vertices have distinct degree pairs is called irregular. Sets of degree pairs for all irregular oriented graphs (also loopless digraphs and pseudodigraphs) with minimum and maximum size are determined. Moreover, a method of constructing corresponding irregular realizations of those sets is given.