As suggested in the comments, you could say
A disjoint union of complete graphs
A graph whose connected components are complete
These graphs are also precisely the graphs whose edges induce an equivalence relation. So rather than study $G$ as a graph, you could study it as a set with an equivalence relation:
Let $G$ be a set with an equivalence relation $\sim$.
This of course assumes that $G$ has no loops, and $a \sim a$ is understood for all $a \in G$.
If $G$ is directed, then the property is a little more interesting;
in this case what you have is basically a set with a preorder:
Let $G$ be a set and let $\le$ be a preorder on $G$.
A directed graph can be understood as a set with a binary relation;
An undirected graph (allowing loops) can be understood as a directed graph whose binary relation is symmetric;
A undirected graph where loops are not allowed can be understood as a directed graph whose binary relation is symmetric and reflexive;
Your property is equivalent to the relation also being transitive.