A non-theological response:
I’m grabbing all the definitions of agapaō from ἀγαπάω, DGE Diccionario Griego-Español, and highlighting those for which they give New Testament or Septuagint instances.
As you can see, there’s a fair area of coverage for the verb; theologians have tried to pin it down in a nice schema, but a concept as vague as “love” is not going to fit nicely.
A ref. to pers.
I 1 welcome with displays of affection (caress, cuddle, etc.), make an affectionate gesture Odyssey; NT.Marc .10.21 (kiss)
• of animals: to caress Plutarch
I 2 fig. Treat with great affection, pamper Xenophon
1 in a relationship between a loving couple: love, caring or affection, in opposition to mere sexual desire Democritus, Plato, Anaxilaus, Aristotle, Dio Chrysostom
• in the LXX with a more general value, freq. in an erotic sense: LXX Ge .29.18, ref. the incestuous desire of Amnon towards Tamar, LXX 2 Kgs .13.1, with. different shades in the same cont. (cf. A II 3 and BI 3) LXX Os .3.1, Ca LXX .1.3, LXX Ca .1.4, LXX Ca .1.7, 3.1-4.
2 more generally: Love, appreciation, esteem mainly towards a king or important person Pindar, Isocrates, Polybius, Dio Chrysostom, Xenophon, Dio Cassius
• towards relatives, esp. children Plato, Xenophon, Dio Chrysoston, Menander LXX Pr.4.3
• esteem of friends, like Isocrates, Aristotle, Dio Chrysostom, in epistolary formulas in papyri
3 of a king or important person: to esteem, appreciate, have in their favour Democritus, Polybius
• from parents to children LXX Ge .25.28.
4 favor, sympathizing, inclination towards people Polybius, Andocides, Aeschines, Isocrates
• empathize, having affinity with Dio Chrysostom
5 of people: to have high appreciation, to liking some, to be fond of someone for their special characteristics or occupations Plato, Xenophon, Dio Chrysostom
III Religious Sense.
1 render funeral honors Euripides
2 of gods: to feel predilection, love ὅτι ἠγάπησέν σε κύριος ὁ θεός σου LXX De .23.6 , cf. Ep.Rom .8.37, Demosthenes, Dio Chrysostom
• esp. ref. to being loved by Hellenistic divinities. freq. of Oriental or Egyptian origin in papyri; Jesus Christ the much loved (by God), the beloved son, Ep.Eph .1.6 1 Ep.Clem .59.2, Dio Chryostom; Jerusalem Rev. .20.9, Inscription
• loving of man towards divinity Dio Chrysostom, cf. LXX De .6.5, 11.1, Ps .30.24, Eu.Matt.22.37 , Josephus, Julian
3 love, driven by not only a religious but philosophical or social imperative, in primitive societies Plato
• in sects or schools, e.g. those following a “Homeric” or Pythagorean life, regard for one’s teachers Plato, Chrysippus
• in Judaeo-Christian literature. LXX Le .19.18, cf. 34, Ev.Io.13.34, Eu.Matt .5.44, Eu.Luc .6.27, 35, Ign. Magn .6.2
• abstract reference to this kind of selfless love 1 Ep.Io. .3.18
• to show love Ev.Io.17.26.
B referring to a thing or action
I 1 liking to do something Odyssey, LXX. Os .12.8, Theopompus
• liking something Plato, Aeschines, Lucian
• have a habit of Aristotle
2 of possessions. Love, crave Plato, Isocrates, Demosthenes, 2 Ep.Petr .2.15
• to wish for, desire Plato, esp. OT and NT LXX Ps .39.17, 2 Ep.Ti .4.8
• with infinitive LXX Ps .33.13 1 Ep.Clem .22.2, τὸ παθεῖν desire martyrdom Ign. Tr .4.2, cf. imperial inscription
3 abstract. Love, cherish, have high price Thrasymachus, Plato, Pseudo-Archytas, Isocrates, Josephus, Xenophon LXX Si .4.12 1 Ep.Petr .3.10
• of perceptions Aristotle
II be happy, content Plato, Isocrates, Demosthenes, Antiphon, Lycurgus, Lucian, Herodian, Alciphron, Thucydides, Xenophon, Aristophanes, Lysias, Aristotle
• in comparative contexts to prefer Xenophon, Demosthenes, Ev.Io.12.43, Plutarch
So DGE identifies, specifically in the New Testament, the following nuances; and note that there’s plenty more nuances even in the Septuagint, let alone Classical literature
- to display affection (kiss)
- love from (a) god
- love towards (a) god
- love as a social imperative
- craving for worldly possessions
- wishing for, desire for something or to do something
- to cherish
- to prefer