Patroclus is like a brother to Achilles, wrathful hero of the Greeks at Troy, and the other half of one of literature’s greatest friendships. When Patroclus dies in battle, wearing his beloved friend’s armour, Achilles laments – Homer tells us in another familial simile – like a lion who has lost his cubs.

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A century or so after The Iliad was written, the authors of the Book of Samuel also turned to the lexicon of family to depict the legendary bond between David and Jonathan. Their affinity is measured not just through comparisons with blood allegiances, but against them: David’s survival hangs on Jonathan’s willingness to betray his father, King Saul, to save his friend. Their story is a contest between the obligations of family and the free choice of friendship.

Achilles and Patroclus, David and Jonathan: these are archetypal double acts, but both are repeatedly and strikingly evoked by reference to other types of relationships. It is as if – then as now – friendship lacked a convincing, independent vocabulary of its own. It isn’t only the authors who turn to analogies and avatars to evoke these characters’ feelings: so do the friends themselves. Achilles insists his terrible, cruel grief for Patroclus could not be more painful were his father to die, or his son. After David kills Goliath, in wordless homage Jonathan “stripped himself of the robe that was upon him, and gave it to David, and his garments, even to his sword, and to his bow, and to his girdle”. Famously, to David their love was “wonderful, passing the love of women”.

This trope of likening friend to family, which writers in different millennia and civilisations have reached for (“Dear as the mother to the son”, Tennyson says of Arthur Hallam in “In Memoriam”, another of friendship’s loveliest testaments), encapsulates a paradox. Without our friendships, life would be thin. On the other hand, from a certain, instrumental point of view, they are inessential, eccentric luxuries, difficult to justify in the common currencies of money, duty and procreation. The comfort of enduring witness and voluntary intimacy that friendships provide, the sense of conducting a two-way experiment in knowing: such benefits are less tangible than those of spouses, children or parents. Friendships derive their value from the ways in which they supplant or compensate for these primary kinships. And authors from Homer onwards have turned to family to describe them.

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That friendships between adults are harder to rationalise than other close relationships may be one reason they are underrepresented in modern fiction, considering their importance in most people’s lives. Film loves friendships, as does television, as the cops and cowboys in buddy movies and series from Butch Cassidy to Cagney and Lacey and Thelma and Louise attest. So do children’s stories, perhaps because, along with the separation from parents with which they coincide, the making and breaking of friendships are among childhood’s first dramas. Think of the beautiful triangle of Winnie the Pooh, Christopher Robin and Piglet. Nineteenth-century authors, especially the Americans, followed friendships across oceans and frontiers; Jane Austen chronicled their tensions and microcrises.

Yet with some noteworthy exceptions – Zadie Smith’s NW, Linda Grant’s Upstairs at the Party, Elena Ferrante – recent adult fiction tends to relegate friendship to the subplot, below the headline concerns of family and romance. It might not help that friendship denies writers the shortcuts they enjoy in the portrayal of other ties. A certain amount of invisible magic is implicit in romantic love, and there is always the fall-back rationale of sex. The axioms of psychoanalysis structure the way we read and think about parents and families. Fictional friendship lacks these conventions.

Achilles, Patroclus, David and Jonathan suggest a rudimentary grammar. In both these stories, as in many robust friendships, there is sameness and difference: Achilles is an infinitely better warrior, but Patroclus is older, wiser and gentler (and a better cook). There is rivalry: if these men measure their friendships against other relationships, they also measure themselves against their friends. In both, the comrades speak hard truths (“you’re impossible”, Patroclus tells Achilles), and share a sense of self-sufficiency, which tips over into an us-against-the-world secrecy and collusion. Friendship may be a free choice, but its costs can be high. Patroclus and Achilles lose their lives; Jonathan risks his own for David, and forfeits his crown. Both partnerships rely as much on the mutual exposure of weakness as on macho virtues, tears as much as swagger. Shared experiences accumulate, all that crying and fighting, such that the men become repositories of each other’s pasts. Then both these heartbreaking friendships are cut short by death – before familiarity curdles into nostalgia, choice morphs into obligation, and, as so often happens in reality, the friendships that were once a counterpoint to more humdrum commitments become almost indistinguishable from them.

AD Miller’s The Faithful Couple is published by Little, Brown.