Understanding the relationship between social and cognitive engagement has critical implications for collaborative learning theory, pedagogy and analytics. This study proposed a three-layered social-cognitive network analysis framework for examining the relationship between students' social and cognitive engagement from summative, epistemic and micro-level perspectives within online collaborative discussions. A multi-method approach was used, consisting of social network analysis, quantitative content analysis, statistical analysis, epistemic network analysis and social-cognitive network visualisation. The results showed that from a summative perspective, students' social participatory roles were critical indicators of their level of cognitive engagement. From an epistemic perspective, socially active students tended to shift towards more group-level cognitive structure, while inactive students showed a decreasing individual-level cognitive structure throughout the discussion duration. From a micro-level perspective, a large proportion of individual students showed continually changing social participatory roles with fluctuating cognitive engagement levels. The findings have implications for collaborative learning theory, pedagogy support and learning analytics.