Do your friends actually like you?

Think of all the people with whom you interact during the course of a day, week, month and year. The many souls with whom you might exchange a greeting or give a warm embrace; engage in chitchat or have a deeper conversation. All those who, by some accident of fate, inhabit your world. And then ask yourself who among them are your friends — your true friends. Recent research indicates that only about half of perceived friendships are mutual. That is, someone you think is your friend might not be so keen on you. Or, vice versa, as when someone you feel you hardly know claims you as a bestie.

It’s a startling finding that has prompted much discussion among psychologists, neuroscientists, organizational behavior experts, sociologists and philosophers. Some blame human beings’ basic optimism, if not egocentrism, for the disconnect between perceived and actual friendships. Others point to a misunderstanding of the very notion of friendship in an age when “friend” is used as a verb, and social inclusion and exclusion are as easy as a swipe or a tap on a smartphone screen. It’s a concern because the authenticity of one’s relationships has an enormous impact on one’s health and well-being.

“People don’t like to hear that the people they think of as friends don’t name them as friends,” said Alex Pentland, a computational social science researcher at Massachusetts Institute of Technology and co-author of a recent study published in the PLOS One journal titled “Are You Your Friends’ Friend? Poor Perception of Friendship Ties Limits the Ability to Promote Behavioral Change.”

The study analyzed friendship ties among 84 subjects (ages 23 to 38) in a business management class by asking them to rank one another on a five-point continuum of closeness from “I don’t know this person” to “One of my best friends.” The feelings were mutual 53 percent of the time while the expectation of reciprocity was pegged at 94 percent. This is consistent with data from several other friendship studies conducted over the past decade, encompassing more than 92,000 subjects, in which the reciprocity rates ranged from 34 to 53 percent.

Pentland said it could be that “the possibility of nonreciprocal friendship challenges one’s self-image.” But the problem may have more to do with confusion over what friendship is. Ask people to define friendship — even researchers like Pentland who study it — and you’ll get an uncomfortable silence followed by “er” or “um.”

“Friendship is difficult to describe,” said Alexander Nehamas, a professor of philosophy at Princeton, who in his latest book, “On Friendship,” spends almost 300 pages trying to do just that. “It’s easier to say what friendship is not and, foremost, it is not instrumental.”

It is not a means to obtain higher status, wangle an invitation to someone’s vacation home or simply escape your own boredom. Rather, Nehamas said, friendship is more like beauty or art, which kindles something deep within us and is “appreciated for its own sake.”

Yet one of the most recognized treatises on friendship is Dale Carnegie’s decidedly instrumental “How to Win Friends and Influence People.” Pop stars like Taylor Swift and Drake are admired for their strategic, if not propagandist, friendships. And, of course, social media sites are platforms for showcasing friendships to enhance personal image.

“Treating friends like investments or commodities is anathema to the whole idea of friendship,” said Ronald Sharp, a professor of English at Vassar College, who teaches a course on the literature of friendship. “It’s not about what someone can do for you, it’s who and what the two of you become in each other’s presence.”

He recalled the many hours he spent in engrossing conversation with his friend Eudora Welty, who was known not only for her Pulitzer Prize-winning fiction but also for her capacity for friendship. Together they edited “The Norton Book of Friendship,” an anthology of works on the topic.

“The notion of doing nothing but spending time in each other’s company has, in a way, become a lost art,” replaced by volleys of texts and tweets, Sharp said. “People are so eager to maximize efficiency of relationships that they have lost touch with what it is to be a friend.”

By his definition, friends are people you take the time to understand and allow to understand you.

Because time is limited, so, too, is the number of friends you can have, according to the work of British evolutionary psychologist Robin I.M. Dunbar. He describes layers of friendship, where the topmost layer consists of only one or two people, say a spouse and best friend with whom you are most intimate and interact daily. The next layer can accommodate at most four people for whom you have great affinity, affection and concern and who require weekly attention to maintain. Out from there, the tiers contain more casual friends with whom you invest less time and tend to have a less profound and more tenuous connection. Without consistent contact, they easily fall into the realm of acquaintance. You may be friendly with them but they aren’t friends.

“There is a limited amount of time and emotional capital we can distribute, so we only have five slots for the most intense type of relationship,” Dunbar said. “People may say they have more than five but you can be pretty sure they are not high-quality friendships.”

Such boasting implies they have soul mates to spare in a culture where we are taught that leaning on someone is a sign of weakness and power is not letting others affect you. But friendship requires the vulnerability of caring as well as revealing things about yourself that don’t match the polished image in your Facebook profile or Instagram feed, said Nehamas at Princeton. Trusting that your bond will continue, and might even be strengthened, despite your shortcomings and inevitable misfortunes, he said, is a risk many aren’t willing to take.

According to medical experts, playing it safe by engaging in shallow, unfulfilling or nonreciprocal relationships has physical repercussions. Not only do the resulting feelings of loneliness and isolation increase the risk of death as much as smoking, alcoholism and obesity; you may also lose tone, or function, in the so-called smart vagus nerve, which brain researchers think allows us to be in intimate, supportive and reciprocal relationships in the first place.

“It’s huge to have good vagal tone, because it modulates our instinctive fight, flight or freeze response,” said Amy Banks, a psychiatrist at the Wellesley Centers for Women who specializes in the growing field of interpersonal neurobiology and is the author of “Wired to Connect: The Surprising Link Between Brain Science and Strong, Healthy Relationships.”

In the presence of a true friend, Banks said, the smart or modulating aspect of the vagus nerve is what makes us feel at ease rather than on guard as when we are with a stranger or someone judgmental. It’s what enables us to feel OK about exposing the soft underbelly of our psyche and helps us stay engaged and present in times of conflict. Lacking authentic friendships, the smart vagus nerve is not exercised. It loses tone and one’s anxiety remains high, making abiding, deep connections difficult.

So it’s worth identifying who among the many people you encounter in your life are truly friends. Who makes time for you? Whose company enlivens, enriches and maybe even humbles you? Whom would you miss? Who would miss you? While there is no easy or agreed upon definition, what friendships have in common is that they shape us and create other dimensions through which to see the world. This can be for better or worse depending on whom we choose as friends. As the saying goes, “Show me your friends and I will show you who you are.”

‘People are so eager to maximize efficiency of relationships that they have lost touch with what it is to be a friend’