graph theory – What does it mean to say ‘nodes greater than [these nodes]’?

I’m confused by a statement in a paper I’m reading. I’ll link below, but the relevant info is as follows:

We have a hypergraph with a set of edges $E$, and we’re iterating through those edges in an algorithm. The offending sentence is:

“For all edges $e_{i} in E$, we call $E X P A N D$ with initial set $Q=e_{i}$, only nodes greater than the nodes of $e_{i}$ are considered as the set $C$ of candidates to expand the current clique, a node $v$ is in $C$ if $forall a_{0}, ldots, a_{r-1} in e_{i}$ the edge formed by $left{a_{0} cup cdots cup a_{r-1} cup vright}$ is in $E$.”

I don’t understand “nodes greater than the nodes of $e_i$“. Does this mean nodes of edges $e_j$, with $j>i$? Or is there some ordering for nodes which I’m missing?

The sentence is in this paper (sorry for the paywall), bottom of page 4.
Thanks!