Is the type of love shared between all heavenly members an affectionate brotherly love mentioned in the Bible? (Catholic perspective) Does the Catholic Church teach that the type of love shared between all heavenly members is an affectionate brotherly love mentioned in the Bible, for example, in Romans 12:10 and 2 Peter 1:5-7?

Below are the verses from Romans 12:10:


  Love one another with mutual affection; outdo one another in showing honour. (NRSV)  
  
  Love one another with brotherly affection; outdo one another in showing honour. (RSV)
  
  (τῇ φιλαδελφίᾳ εἰς ἀλλήλους φιλόστοργοι τῇ τιμῇ ἀλλήλους προηγούμενοι.)


Below are the verses from 2 Peter 1:5-7 (emphasis added):


  For this very reason make every effort to supplement your faith with virtue, and virtue with knowledge, and knowledge with self-control, and self-control with steadfastness, and steadfastness with godliness, and godliness with brotherly affection, and brotherly affection with love.
In 1 John 4:8, (God is love) the Greek word used for love is agapē. Given that the verse refers to 'God' rather than 'the Father' or 'the Son', one could assume it is referring to God as the Trinity. Thus, the members of the Trinity (God) probably share agapē love.
[agape being the highest and most unconditional form of love]