What defines a group of friends? Rethinking community structure in signed, directed networks

TL;DR

This study analyzes the complex structure of friendships and conflicts among high school students using a signed, directed network model, revealing diverse community patterns and the influence of relationship attributes on group organization.

Contribution

It introduces a Bayesian stochastic block model approach to analyze signed, directed networks without prior assumptions, uncovering nuanced community structures and the roles of tie attributes.

Findings

Mutual affinities form statistically coherent clusters.

Asymmetric ties are common within and between communities.

Intense ties significantly influence community structure.

Abstract

We study the structure of personal relationships among 1068 high school students using a dataset that contains the network of self-reported friendly and conflictive relationships, with information on their directionality and intensity. We analyse the resulting weighted, directed, and signed network using a Bayesian stochastic block model framework, which enables the inference of group structure without imposing prior assumptions on the role of negative or asymmetric ties. While a full model incorporating all edge attributes yields statistically coherent clusters, these do not align with socially meaningful communities. To address this, we focus first on the network backbone of mutual affinities, and we characterize its group organization. Many communities display an assortative structure, often embedded within larger cohesive configurations, but we also observe more diverse patterns such as core-periphery structure and isolated nodes. We then examine how relationship intensity, directionality, and conflict shape group structure. Asymmetric ties, though often occurring between communities, are frequently present within them, revealing the stabilizing effect of group membership on non-mutual relationships. Furthermore, the presence of asymmetric ties does not inherently imply a hierarchical structure, given that all groups both receive and report significant levels of non-reciprocal ties. More intense ties play a disproportionate role in shaping community structure. Finally, negative ties tend to bridge communities, but we find that groups feature a significant level of internal conflict. Our research offers a new perspective on the study of group organization when rich information about the directionality, the intensity and the sign of ties is considered, with implications for identifying social vulnerability and designing targeted interventions.