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We are arguing about the following phrase:

"Being the density of the graph a common requirement, both for the regularity lemma and for meaningful metric estimators in large graphs, our experiments are addressed to answer two scientific questions: ..."

Our friend asserts that the correct sentence is

"The density of the graph being a common requirement, both for the regularity lemma and for meaningful metric estimators in large graphs, our experiments are addressed to answer two scientific questions: ..."

Which one is the correct choice?

  • Your friend's version looks correct. In your version, "being the density of the graph" sounds like "since (whatever went before) is the density of the graph", which leaves the phrase "a common requirement" dangling without saying what the requirement is. – Lawrence Mar 8 '17 at 11:38
  • There is no previous phrase. This is the starting paragraph. – AreTor Mar 8 '17 at 11:47
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    That only weakens your case. You might be thinking of the construction "Being that ...". – Lawrence Mar 8 '17 at 11:49
  • There might be a way to argue that yours is "legal" syntax, but it's very strange and non-standard, at the very least. Note that if you said "... graph is a common..." that would be fine (though the sentence is still complex enough to require reading twice). – Hot Licks Mar 8 '17 at 12:26
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Your first option doens't mean what I think you think it means :)

Being the density of the graph a common requirement, [...] our experiments are addressed to answer two scientific questions: ...

This means that your experiments are "the density of the graph [,] a common requirement" – this doen't make much sense.

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Your version is at best extremely eccentric word order. Your friend's is very nice. Sorry to tell you that!

This is what I would call an absolute construction, by the way. In general, the verb "to be" will come between its subject and its "object" (though to call it an object is to oversimplify slightly).

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