5,836 research outputs found
A parent-centered radial layout algorithm for interactive graph visualization and animation
We have developed (1) a graph visualization system that allows users to
explore graphs by viewing them as a succession of spanning trees selected
interactively, (2) a radial graph layout algorithm, and (3) an animation
algorithm that generates meaningful visualizations and smooth transitions
between graphs while minimizing edge crossings during transitions and in static
layouts.
Our system is similar to the radial layout system of Yee et al. (2001), but
differs primarily in that each node is positioned on a coordinate system
centered on its own parent rather than on a single coordinate system for all
nodes. Our system is thus easy to define recursively and lends itself to
parallelization. It also guarantees that layouts have many nice properties,
such as: it guarantees certain edges never cross during an animation.
We compared the layouts and transitions produced by our algorithms to those
produced by Yee et al. Results from several experiments indicate that our
system produces fewer edge crossings during transitions between graph drawings,
and that the transitions more often involve changes in local scaling rather
than structure.
These findings suggest the system has promise as an interactive graph
exploration tool in a variety of settings
Fractal and Transfractal Recursive Scale-Free Nets
We explore the concepts of self-similarity, dimensionality, and
(multi)scaling in a new family of recursive scale-free nets that yield
themselves to exact analysis through renormalization techniques. All nets in
this family are self-similar and some are fractals - possessing a finite
fractal dimension - while others are small world (their diameter grows
logarithmically with their size) and are infinite-dimensional. We show how a
useful measure of "transfinite" dimension may be defined and applied to the
small world nets. Concerning multiscaling, we show how first-passage time for
diffusion and resistance between hub (the most connected nodes) scale
differently than for other nodes. Despite the different scalings, the Einstein
relation between diffusion and conductivity holds separately for hubs and
nodes. The transfinite exponents of small world nets obey Einstein relations
analogous to those in fractal nets.Comment: Includes small revisions and references added as result of readers'
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