Love is. It does not ever try to prove itself, because it is. If you have true love, you will never be lonely; you will never lack genuine and unfeigned love. True love is selfless and strives to take care of everyone else first. In this way it propagates agape and provides for the one who loves and the beloved.
The person who loves in truth gets the benefit of their own love; their own love ministers to them. It is like a mother feeding her child, yet both of them become full. Again, it's like filling one sack from another, but both of them become full. Love is infinite, because God is Love. If our love is infinite and we give away an infinite amount of love, we still have an infinite amount of love. Do you see the mystery of love? Don't horde your love, or you will run out; that is the life of misery and despair.
Love is. Stop trying to prove your love. Don't choosing substitutes to love instead of the true path. Don't grooming your outward appearances so that people will like you or even worse lust after you. Instead, become concerned with doing good to the souls of others, ministering to people's hearts, wiping away their despair and people will love you. Propagate the love of God; propagate agape.
"Every art and every inquiry, and similarly every action and choice, is thought to aim at some good; and for this reason the good has rightly been declared to be that at which all things aim." ~Aristotle~