  Sankey diagram is popular for analyzing primary flows in network data.
However, the growing complexity of data and hence crossings in the diagram
begin to reduce its readability. In this work, we studied the NP-hard weighted
crossing reduction problem of the Sankey diagram with both the common parallel
form and the circular form. We expect to obtain an ordering of entities that
reduces weighted crossings of links. We proposed a two-staged heuristic method
based on the idea of barycentre ordering and used Markov chain to formulate the
recursive process of obtaining such ordering. In the experiments, our method
achieved 300.89 weighted crossings, compared with the optimum 278.68 from an
integer linear programming method. Also, we obtained much less weighted
crossings (87.855) than the state-of-art heuristic method (146.77). We also
conducted a robust test which provided evidence that our method performed
consistently against the change of complexity in the dataset.
