"…and the Latin, Augustinian approach to God as a simple essence, within which a Trinity of persons can be understood only in terms of internal relations." - Byzantine Theology, pg 61 by John Meyendorff.
My point is that I don't see relation and communion as concepts alien to each other. It seems to me that Meyendorff is making a distinction between the understanding of relations in the West and personalism in the East.
I could be wrong, because I neither have the book (and therefore no context) or remember enough of it from my one and only attempt over ten years ago, but I don't think it's a distinction between "relations" and "personalism".
I think what he's talking about is the Western tendency (whether it's accurate or a stereotype, I can't say for sure) to identify the "unity" of the three persons in their common essence (i.e., divinity). "God" is one because this essence is one. How, then, do you reconcile the "threeness" that is fundamental to the Christian faith? The three persons are divine because they possess this essence, and this "relates" them to each other. We distinguish one from the others by these relations, but the three are one because of the unity of the essence:
For with your Only Begotten Son and the Holy Spirit
you (i.e., the Father) are one God, one Lord:
not in the unity of a single person,
but in a Trinity of one substance.
Roman Missal, Preface of the Holy Trinity
The Church, however, identifies the source of the unity of the three persons in a person--the Father--and not in their common essence (divinity). The Father is unoriginate, he eternally begets the Son, and he eternally "breathes forth" the Spirit proceeding from him. They are co-essential (they share the same essence), and there never was a time when the Son or the Holy Spirit did not exist, but it is the person of the Father which is the principle of unity. The Father is God, the Son is God, and the Holy Spirit is God, but God (ὁ Θεός) is the Father.