The diffusion process of linguistic innovations has long been a topic of interest in sociolinguistics (Weinreich et al., 1968) and many studies have highlighted the influence of social structures on change (Labov, 2001; Milroy & Milroy, 1997). The recent access to massive social network data and the advent of computational sociolinguistics (Nguyen et al., 2016) allow an approach to this phenomenon that combines a large amount of data and a fine-grained temporality. Using methods from both computational sociolinguistics and network science, we focus on the diffusion of lexical innovations and we ask what differentiates, after an expansion phase, those that stabilize within our observation period from those that are eventually abandoned. In particular, we examine the impact of the social structure of linguistic communities on these diffusion and acceptance processes. We rely on a corpus of French tweets, that spans from 2012 to 2019 and includes about 600 million tweets from more than two million users. Based on the evolution over time of the rate of use of each linguistic form, we select those that appear during the period covered by the corpus and then we distinguish the forms that stabilize from those that eventually die out. By modeling the trajectories, we then identify the three characteristic periods of the diffusion of an innovation (Fagyal et al., 2010). Finally, by establishing the network of contact between users on the basis of their followers and followees, we examine the circulation of forms between them at different periods, and identify factors that condition the stabilization or not of innovations. This poster will present the methodologies used to identify linguistic innovations and to model their trajectory. We will also present the first results on the connection between the evolution of forms and the structure of the contact network.