Force-directed graph visualization with pre-positioning : improving convergence time and quality of layout

![CDATA[Modern visual analytics tools provide mechanism for users to gain unknown knowledge through effective visual interactions for user to quickly understand the progress of algorithms and adjust the input parameters on intermediate visualizations that towards the production of most satisfied outcome. This requires the quick production of a sequence of graph visualizations. However, the traditional force-directed graph drawing algorithms are very slow to reach an equilibrium configuration of forces. They usually spend tens of seconds producing the layout of a graph converge. Thus, they do not satisfy the requirement of rapid drawing of graphs. This paper proposes a fast convergence method for drawing force-directed graphs. We essentially pre-calculate the geometrical position of all vertices before applying a force-directed layout algorithm to reach the energy minimization of the graph layout. The experimental results have shown that this approach could not only reduce the convergence time but also the number of edge crossings that approves the quality of layout significantly.]]