This is such an excellent question that has been much neglected. See the appendix below for a general discussion about love in its various aspects. The NT teaching about agape love can be summarized as follows:
God is Love, 1 John 4:8, 16. This teaches that God, at His inner core and essential essence is love. Such love is other-focused and since God is eternal, so is love. This is principled love - not based on sentimentality but a firm decision to love someone who may or may not deserve such love as proven in John 3:16.
All true love come from God.
- 1 John 4:7, 8 - Beloved, let us love one another, because love comes from God. Everyone who loves has been born of God and knows God. Whoever does not love does not know God, because God is love.
- 1 John 5:1 - Everyone who believes that Jesus is the Christ is born of God, and everyone who loves the father loves his child as well.
- Rom 8:39 - neither height nor depth, nor anything else in all creation, will be able to separate us from the love of God that is in Christ Jesus our Lord.
- 1 John 4:9, 10 - This is how God’s love was revealed among us: God sent His one and only Son into the world, so that we might live through Him. And love consists in this: not that we loved God, but that He loved us and sent His Son as the atoning sacrificed for our sins.
- We love because God loved us
- 1 John 4:11 - Beloved, if God so loved us, we also ought to love one another.
- 1 John 4:12 - No one has ever seen God; but if we love one another, God remains in us, and His love is perfected in us.
- 1 John 4:19 - We love because He first loved us.
- 1 Thess 4:9 - Now about brotherly love, you do not need anyone to write to you, because you yourselves have been taught by God to love one another.
- 1 John 3:23 - And this is His commandment: that we should believe in the name of His Son, Jesus Christ, and we should love one another just as He commanded us.
- The love of God we show others in manifested in various ways
- John 13:34, 35 - A new commandment I give you: Love one another. As I have loved you, so you also must love one another. By this everyone will know that you are My disciples, if you love one another.”
- John 14:15 - If you love Me, you will keep My commandments. [Note that the verb, "will keep" is not imperative but future indicative suggestion that love for God is what induces obedience to God's commends.]
- John 15:12, 13, 17 - This is My commandment, that you love one another as I have loved you. Greater love has no one than this, that he lay down his life for his friends. [That is, just as Jesus did.] ... This is My command to you: Love one another.
- Eph 5:1, 2 - Be imitators of God, therefore, as beloved children, and walk in love, just as Christ loved us and gave Himself up for us as a fragrant sacrificial offering to God.
- Eph 5:24 - Husbands, love your wives, just as Christ loved the church and gave Himself up for her.
- 1 John 4:12 - No one has ever seen God; but if we love one another, God remains in us, and His love is perfected in us.
- Rom 12:10 - Be devoted to one another in brotherly love. Outdo yourselves in honoring one another.
- 1 Thess 3:12 - And may the Lord cause you to increase and overflow with love for one another and for everyone else, just as our love for you overflows,
- Heb 10:24 - And let us consider how to spur one another on to love and good deeds.
- 1 Peter 4:8-10 - Above all, love one another deeply, because love covers over a multitude of sins. Show hospitality to one another without complaining. As good stewards of the manifold grace of God, each of you should use whatever gift he has received to serve one another.
- 2 John 5, 6 - And now I urge you, dear lady—not as a new commandment to you, but one we have had from the beginning—that we love one another. And this is love, that we walk according to His commandments.
- 1 Peter 3:8 - inally, all of you, be like-minded and sympathetic, love as brothers, be tenderhearted and humble.
The meaning in John 15:12 is subtle - if we are loving, we reflect God's love for us. However, I would not press this to far as John was overly strict in the way he used such rare verb-forms.
APPENDIX - Love in the NT
The Bible does not discuss just one type of love but clearly recognizes several kinds. The Greek language had six words for various kinds of love, but only three of these broad categories are discussed here. They are arranged into a kind of hierarchy – the widest first and the narrowest last.
“Agape” love (Greek: agapao (v) or agape (n))
This is the most general kind of love and does not necessarily involve any sentimentality, feelings nor whim. Nor does this kind of love necessarily involve liking somebody. It springs purely from principle and is often opposed to the natural inclinations. This dependable, abiding and constant love is celebrated in 1 Cor 13. It is others-focused so excludes all self-centredness.
The best definition of agape love is, “God so loved … that He gave His son …” (John 3:16). The “agape” love is the central most important characteristic, the very essence, of God (1 John 4:8, 16). Love’s outward manifestation is grace. It is God as love that defines God and all else about Him such as justice/righteousness tempered with kindness.
This principled love of God (1 John 4:8, 16) is to be imitated by all Christians (John 13:34, 35) and is motivated by God’s love for us (1 John 4:9, 10, 19-21, 2 Cor 5:14). Thus, love is quintessentially Christian and reached its zenith when God gave Jesus as the solution to the sin problem (2 Cor 5:14, Eph 2:4, 3:19, 5:2, John 3:16). Therefore, Christians should have as their primary focus their love of, and love to God (Matt 22:37, Deut 6:5), and secondarily love to fellow humans (Matt 22:39, Lev 19:18).
This word is used to describe God’s love to Jesus (John 17:26) and humankind generally (John 3:16, Rom 5:8). It also describes the love that Christians should have to all people (1 Thess 3:12, 1 Cor 16:14, 2 Peter 1:7).
From this agape love springs all else and expresses itself in obedience to God’s commandments (John 14:15, 21, 23, 15:10, 1 John 2:5, 5:3, 2 John 6). Love is the root of respect for others’ opinions and choices; thus it is also the basis for freedom of choice (which see) and freedom of religion (which see).
Isa 63:9 expresses the kind of empathetic love that God has for each person.
In all their distress he too was distressed, and the angel of his
presence saved them. In his love and mercy he redeemed them; he lifted
them up and carried them all the days of old.
Friendship, Affection (Greek: phileo (v) or philos (n))
Friendships arise between people who have some kind of common interest. Affection may arise from a deeper friendship where greater closeness and some physical contact is appropriate. Thus, affection exists between family members, close friends, or even pets, etc. In the New Testament the word most commonly represents tender affection. (Its close cognate relative, “philema”, means, “kiss”.)
The word is used to describe the love of the Father for Jesus (John 5:20) and the believing Christian (John 16:27, 20:2).
In the New Testament, this philos love is never used in a command of men to love God.
Erotic Love (Greek: eros (n))
Erotic love involves sexual intimacy which, within a marriage, is highly praised in the Bible but condemned outside marriage. The book “Song of Solomon” is a celebration of this kind of love.
The hierarchy of love means that agape-love is a necessary pre-requisite to friendship and affection, and that friendship is a necessary prerequisite to erotic love (SS 5:16). It is the frequent inversion of this hierarchy in modern culture that has created so much interpersonal tension and societal difficulties, and directly leads to the oxymoron of selfish love. Such would be impossible if our love had its proper origin in divinely inspired agape love.