This study applied the question-oriented problem-solving (QOPS) pedagogy in Statistics learning and addressed several methodological and theoretical gaps in SNA studies to inform instructional and learning implications for teachers and students. The limitations in SNA studies included the lack of theoretical support in the analysis, the homogeneous medium where the data for SNA is collected, the constraints in the diversity of the network modes, and the lack of associations about the SNA measures with learning outcomes. Thus, we investigated 1) how a learning community based on social media evolved with the implementation of the QOPS activities, 2) changes in instructors and learners' roles in light of their one-mode and two-mode SNA measures, and 3) how different relational ties and SNA measures were associated with student outcomes. Participants were 23 graduate students (females: 52.17%) and an instructional team of three. Seven hundred four messages, including 118 posts and 586 comments, were collected from the private advanced statics Facebook learning group over an 18-week advanced Statics course. Aligned with the QOPS approach, the learning community became more interactive and cohesive, as reflected in their one-mode SNA measures. Besides, the two-mode measures, including density, GCC, reciprocity, transitivity, and strong/weak components, demonstrated that the learning community became denser and more interactive via their shared discussion. The instructional team played unique roles as a leader or facilitator in their interaction with students, while students' roles as a leader and coordinator were identified. Students' outdegree, degree, and closeness centralities have the most consistent predictive validity of their learning outcomes. Higher values in degree or closeness via shared discussion topics such as discussion of quizzes, help-seeking, and course administrative communication also predicted performance. The study results have practical implications for instructors and researchers in designing the hybrid learning environment and providing scaffolds to promote help-seeking.