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 $\left\{a_{0} \cup \cdots \cup a_{r-1} \cup v\right\}$ 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!