Friendship networks and social status

TL;DR

This paper analyzes friendship networks among students, revealing a consistent pattern where unreciprocated friendships mostly go from lower to higher-ranked individuals, reflecting social status.

Contribution

It introduces a maximum-likelihood method to infer social rankings from directed friendship networks, highlighting their relation to social status and other characteristics.

Findings

Unreciprocated friendships mostly flow from lower to higher-ranked individuals.

Rankings correlate with age and popularity, indicating social status.

Different statistics for reciprocated and unreciprocated friendships suggest different formation processes.

Abstract

In empirical studies of friendship networks participants are typically asked, in interviews or questionnaires, to identify some or all of their close friends, resulting in a directed network in which friendships can, and often do, run in only one direction between a pair of individuals. Here we analyze a large collection of such networks representing friendships among students at US high and junior-high schools and show that the pattern of unreciprocated friendships is far from random. In every network, without exception, we find that there exists a ranking of participants, from low to high, such that almost all unreciprocated friendships consist of a lower-ranked individual claiming friendship with a higher-ranked one. We present a maximum-likelihood method for deducing such rankings from observed network data and conjecture that the rankings produced reflect a measure of social status. We note in particular that reciprocated and unreciprocated friendships obey different statistics, suggesting different formation processes, and that rankings are correlated with other characteristics of the participants that are traditionally associated with status, such as age and overall popularity as measured by total number of friends.