The second part of Revelation 2: 7 is a good example of why finding the subject of a sentence is important. For one thing, it is not always expressed separately in Greek, as we see below:
τῷ νικῶντι δώσω αὐτῷ φαγεῖν ἐκ τοῦ ξύλου τῆς ζωῆς, ὅ ἐστιν ἐν τῷ παραδείσῳ τοῦ θεοῦ.
to the victorious one I will give to him to eat from the tree of life, which is in the paradise of God
Since I have translated this more or less word for word, the English is awkward, but should be understandable.
So where is the subject? The main verb is δώσω – ‘I will give’, and the subject is thus ‘I’, but not expressed with a separate Greek word. The basic framework of the sentence is:
(When a Greek subject is not separately expressed my habit is to put the English translation in parentheses on the subject line. This avoids leaving the space blank or filling in with a Greek word that isn’t found in the sentence.)
What is being given? In this case we can think of the infinitive φαγεῖν (‘to eat’) as the direct object of δώσω. Some English translations make this relationship clearer than others; the NIV, for example, reads ‘I will give the right to eat’. And who has been given this right? For the indirect object we must return to the beginning of the sentence: ‘τῷ νικῶντι’ (‘to the victorious one’).
Here is the diagram:
The rest of the sentence includes phrases which modify this basic structure. ‘From the tree of life’ answers the question ‘to eat what?’, and is a prepositional phrase modifying φαγεῖν. In my own studies (I don’t pretend this is approved diagramming procedure) I would simply add this to the direct object, as below:
Finally, let’s briefly consider what do with do with the phrase
ὅ ἐστιν ἐν τῷ παραδείσῳ τοῦ θεοῦ
which is in the paradise of God
The part of the sentence has its own internal structure, something like this,
where the prepositional phrase ἐν τῷ παραδείσῳ τοῦ θεοῦ is linked (slanted line) as a description of the subject, in this case describing its location. The entire clause modifies τοῦ ξύλου τῆς ζωῆς, and here is a stab at a diagram of the sentence as a whole:
Once again, the purpose of diagramming a koine sentence is not to become enmeshed in detail, but to make the underlying grammatical structure more obvious, as an aid to understanding.