2012/05/30 by B. Ball, Brian Ball, M. E. J. Newman · 145 citations
Computer Science · Mathematics · Physics and Astronomy · Psychology · Social Sciences · #Artificial intelligence #Complex Network Analysis Techniques #Computer science #Friendship #Mathematics #Opinion Dynamics and Social Influence #Popularity #Psychology #Ranking (information retrieval) #Social Capital and Networks #Social media #Social network (sociolinguistics) #Social psychology #World Wide Web #cs.SI #physics.soc-ph
paper · pdf · doi:10.1017/nws.2012.4
published in Network Science 1(1), 16-30 (Cambridge University Press) · 7 pages, 6 figures
arxiv created 2012/05/30 · openalex publication_date 2013/04/01 · arxiv updated 2014/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.