Love for Plato is that which is part of a relationship. It is the the love of wisdom and learning that is greatest. Socrates is said to have constantly repelled all sexual love advances, and says that he knows what he can give in the relationship, wisdom, but that the other can only give beauty then is not equal. For love is an equal relationship that is based on dialauge and love of the good. The process is that first the love is of someone that is beautiful. Then comes a love of beauty itself, and the desire that all be able to know this love. Love then becomes teaching and learning and the beauty of wisdom.
Love is what drives Neo in all that he does. First it is a love of another, and through this he is able to love himself, sort of. But he still is not ready and has a lot of fear. He is alone with Trinity will everyone else is at the party in the cave. He is the One, but he is still doing everything out of his love for Trinity. He does not really love himself yet. Love is a motivator for most of the characters in the Matrix. From Link, to Morpheus, to Niobe, the counselors, the people who fight for Zion. Love drives all of them.
Neo learns that the programs can love when the two programs are trying to smuggle their daughter into the Matrix to escape deletion. They have the feeling or connection that the word love means or describes. Neo uses this to go into the machine city and try to broker a peace between humans and machines. He appeals to their empathy.
Love in the Matrix is physical and focused at first. This is Neo and Trinity. Then comes a sense of duty and wanting the good for another. Trinity when she goes in the Matrix to save Neo. She gives herself for another. This is also exemplified in all those who are fighting to stay alive and for survival. Finally there is an acceptance and a love of that which greater than each one separately. Love is also what the Oracle uses to unbalance the equation. She is like Diotima, pushing and proding those she encounters toward a purpose that she knows but not for certain, and using love of the good to accomplish her task.