Static Layout MethodsFig. 1: Our approach in using persistent homology to untangle force-directed layouts has two main functionalities. First, as demonstrated via the HIC 1K NET dataset, we use persistent homology to formulate an initial graph layout (column 1) that improves both the convergence rate of the graph layout and the final layout quality. Second, our approach comes with interactive capabilities, as illustrated in Fig. 2. We use the local continuity meta criterion (Q LCMC ) for layout evaluation (larger is better). In terms of convergence, our approach (column 2, rows 2 and 3) shows the formation of major graph structures as early as 5 iterations, whereas the standard approach (column 4, row 1) takes 25+ iterations. In terms of final layout quality, the Q LCMC scores for the final layout (column 5) show that our approach significantly exceeds the standard one. Three static layout methods, neato, fdp, and sfdp, are also included for comparison (column 6), with only sfdp (column 6, row 3) showing a comparable Q LCMC score.
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