I found this article by Murphy
pointing to work by Almaatouq et al.
to align with my recent experience of having two long term friends (or so I thought), simply stop responding to emails about getting together. And, from the other direction, being described as "our good friend" by a couple I didn't particularly like. It turns out that studies show that only about half of perceived friendships are mutual. The Alamaatouq et al. 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 percent to 53 percent.
Clips from the last portion of Murphy's article:
Because time is limited, so, too, is the number of friends you can have, according to the work of the 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.
...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...In the presence of a true friend...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 O.K. 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.
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