text: We adapt multilevel, force-directed graph layout techniques to visualizing dynamic graphs in which vertices and edges are added and removed in an online fashion (i.e., unpredictably). We maintain multiple levels of coarseness using a dynamic, randomized coarsening algorithm. To ensure the vertices follow smooth trajectories, we employ dynamics simulation techniques, treating the vertices as point particles. We simulate fine and coarse levels of the graph simultaneously, coupling the dynamics of adjacent levels. Projection from coarser to finer levels is adaptive, with the projection determined by an affine transformation that evolves alongside the graph layouts. The result is a dynamic graph visualizer that quickly and smoothly adapts to changes in a graph.
  @cite_11: On-line graph drawing deals with huge graphs which are partially unknown. At any time, a tiny part of the graph is displayed on the screen. Examples include web graphs and graphs of links in distributed file systems. This paper discusses issues arising in the presentation of such graphs. The paper describes a system for dealing with web graphs using on-line graph drawing.
summary: The key frame approach can be adapted to address the online problem by computing a new key frame each time a request arrives, and then interpolating to the new key frame. For example, @cite_11 developed a system for browsing large, partially known graphs, where navigation actions add and remove subgraphs. They use force-directed layout for key frame graphs, and interpolate between them.