In a 2-regular graph, every node sits on precisely two edges; it has “degree 2.” In a 600-regular graph, each node has degree 600. If you start again with your 100 dots and keep adding edges, a ...

Graphical Regular Representation (GRR): A Cayley graph whose automorphism group acts regularly on its vertex set, meaning each automorphism is uniquely determined by its effect on a single vertex.

Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is ...

The size of the smallest edge cut-set (cohesion) and the size of the smallest node cut-set (connectivity) have been used by some authors as vulnerability measures of a graph. Generalizations of the ...