# 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!