This paper adapts a graph-based analysis and visualisation tool, search trajectory networks (STNs) to multi-objective combinatorial optimisation. We formally define multi-objective STNs and apply them to study the dynamics of two state-of-the-art multi-objective evolutionary algorithms: MOEA/D and NSGA2. In terms of benchmark, we consider two- and three-objective ρmnk-landscapes for constructing multi-objective multi-modal landscapes with objective correlation. We find that STN metrics and visualisation offer valuable insights into both problem structure and algorithm performance. Most previous visual tools in multi-objective optimisation consider the objective space only. Instead, our newly proposed tool asses algorithm behaviour in the decision and objective spaces simultaneously.