Question on Dataset isSmaller(G,H)

[uvdsl]

Hi,
I am currently trying to understand the algorithms better - your code helps a lot! Thank you very much.

While implementing my own interpretation of the algorithm, I stumbled upon the ordering of graphs, which you have implemented in the Dataset as isSmaller.

As I understood from the paper, the ordering itself was not specified so you had to come up with your own:

G < H if and only if G ⊂ H or there exists a triple t ∈ G \ H such that no triple t' ∈ H \ G exists where t' < t .

You implemented a shortcut with

// If HmG, i.e., H\G is empty then the second predicate is trivially true, so we are also done
 if( HmG.length === 0 ) return true;

While your implementation does exactly what you defined, I was wondering - more generally - the follwoing:
Let G = { (s,p,o), (s,p,x) } a graph consisting of two triples.
Let H = { (s,p,o) } a graph consisting of one triple such that H is a true subgraph of G.
Then:
GmH = {(s,p,x)} and HmG = { }.
Now, isSmaller(G,H) will return true as HmG is empty, just as you defined.

However, isSmaller(H,G) will also return true as H is a true subgraph of G, just as you defined.

Intuitively, I would have expected to first check for true subgraphs in both directions and second if none is a true subgraph of the other then to check if all triples in GmH are (lexicographically) smaller than all triples in HmG otherwise G is not smaller than H.

So, in a nutshell, I was expecting the check if H is subgraph of G, instead of the shortcut. The rest is fine to my understanding.
So: if( HmG.length === 0 ) return false;

Am I missing something? I would appreciate any clarifications and explanations why I am totally wrong about this :)
Cheers
Christoph