# Definition and usage of "Non-reciprocal"

What is the precise meaning of "non-reciprocal?" Two definitions of "reciprocal" taken from the Merriam-Webster dictionary are:

• shared, felt, or shown by both sides
• serving to reciprocate : consisting of or functioning as a return in kind

The definition provided in the dictionary of non-reciprocal is essentially just 'not reciprocal.' This raises some questions relating to existential qualifiers and colloquial usage. Consider the following statements:

1. Alice likes Bob while Bob likes Alice
2. Alice likes Bob while Bob dislikes Alice
3. Alice likes Bob while Bob is ambivalent towards Alice

Clearly, statement 1 describes a reciprocal relationship between Alice and Bob. If we are given the information that statement 1 is not true, we cannot infer whether statements 2 or 3 are true. In a strict logical sense, if the relationship between Alice and Bob is non-reciprocal, it is not possible to distinguish whether statements 2 or 3 are true, but I have heard people use non-reciprocal to refer sometimes to statement 2 or sometimes to statement 3.

Are there any clear guidelines or more specific definitions for usage of the word 'non-reciprocal'?

Thank you.

• In a directed graph where an edge from A to B means A loves B, not having an edge from A to B does not mean that A hates B (although she could hate him). So I don't see how you can conclude anything about general reciprocal relationships from directed graphs. Jul 20, 2023 at 2:32
• It seems as if you should focus on the meaning of "reciprocal". Preceding it with "non-" simply negates whatever that is, without being more specific. Jul 20, 2023 at 3:17
• Are you asking about its meaning in graph theory or in the context of interpersonal relationships? Mathematical terminology rarely corresponds to everyday English. Jul 20, 2023 at 3:26
• (I think "reciprocated" is more common than "reciprocal" in such contexts, no?) Jul 20, 2023 at 3:27
• @PeterShor I am particularly interested in usage in the context of statistical physics. The reference to graphs is somewhat irrelevant to my interest; it was not a good choice to include it. In a recent paper titled “Non-reciprocal phase transitions” by Fruchart, et al., ‘non-reciprocal’ seems to refer to something like case 2 in my post. alphabet asks whether I am interested in everyday or mathematical contexts. I cannot find a precise definition of ‘non-reciprocal’ in physics, so I am curious how it might be used in more formal contexts that may not involve precise mathematical definitions. Jul 20, 2023 at 5:22