From Population Diversity to Contact Diversity: A Network-Based Generalization of the Greenberg Index

Quantifying linguistic diversity is central to the analysis of multilingual societies, yet widely used measures such as the Greenberg Diversity Index abstract from patterns of social interaction. As a result, demographic diversity may diverge substantially from the diversity individuals actually experience through everyday contact. This paper introduces the Network-based Greenberg Diversity Index (N-GDI), which measures linguistic diversity at the level of social ties rather than population composition. The index is defined as the probability that a randomly selected interaction connects speakers of different languages, thereby capturing realized or contact-based diversity. We formally relate the N-GDI to the classic Greenberg index and to standard network measures of mixing, and we develop extensions that condition contact diversity on linguistic competences and on multiple interaction domains. Using simulations on stylized network archetypes, we show that populations with identical demographic diversity can exhibit markedly different levels of contact diversity depending on interaction structure. Bridging ties, network centralization, and domain-specific interaction patterns systematically affect the gap between potential and realized diversity. Competence-conditioned simulations further demonstrate that increased bilingualism reduces communicative distance without necessarily increasing social mixing. By distinguishing demographic diversity, structural exposure, and communicative overlap, the proposed framework provides a simple and interpretable tool for computational social science and for the evaluation of language policies. It highlights how interaction structures shape multilingual experience and offers a diagnostic perspective on whether limited exposure arises from segregation or from lack of shared linguistic resources.