In this study, we explore peer-interaction effects in online networks on speaking skill development. In particular, we present an evidence for gradual buildup of skills in a small-group setting that has not been reported in the literature. We introduce a novel dataset of six online communities consisting of 158 participants focusing on improving their speaking skills. They video-record speeches for 5 prompts in 10 days and exchange comments and performance-ratings with their peers. We ask (i) whether the participants' ratings are affected by their interaction patterns with peers, and (ii) whether there is any gradual buildup of speaking skills in the communities towards homogeneity. To analyze the data, we employ tools from the emerging field of Graph Signal Processing (GSP). GSP enjoys a distinction from Social Network Analysis in that the latter is concerned primarily with the connection structures of graphs, while the former studies signals on top of graphs. We study the performance ratings of the participants as graph signals atop underlying interaction topologies. Total variation analysis of the graph signals show that the participants' rating differences decrease with time (slope=-0.04, p<0.01), while average ratings increase (slope=0.07, p<0.05)--thereby gradually building up the ratings towards community-wide homogeneity. We provide evidence for peer-influence through a prediction formulation. Our consensus-based prediction model outperforms baseline network-agnostic regression models by about 23% in predicting performance ratings. This, in turn, shows that participants' ratings are affected by their peers' ratings and the associated interaction patterns, corroborating previous findings. Then, we formulate a consensus-based diffusion model that captures these observations of peer-influence from our analyses.