Languages show substantial variability between their speakers, but it is currently unclear how the structure of the communicative network contributes to the patterning of this variability. While previous studies have highlighted the role of network structure in language change, the specific aspects of network structure that shape language variability remain largely unknown. To address this gap, we developed a Bayesian agent‐based model of language evolution, contrasting between two distinct scenarios: language change and language emergence. By isolating the relative effects of specific global network metrics across thousands of simulations, we show that global characteristics of network structure play a critical role in shaping interindividual variation in language, while intraindividual variation is relatively unaffected. We effectively challenge the long‐held belief that size and density are the main network structural factors influencing language variation, and show that path length and clustering coefficient are the main factors driving interindividual variation. In particular, we show that variation is more likely to occur in populations where individuals are not well‐connected to each other. Additionally, variation is more likely to emerge in populations that are structured in small communities. Our study provides potentially important insights into the theoretical mechanisms underlying language variation.