Visualizing the temporal evolution of dynamic networks

Kevin S. Xu, Mark Kliger, and Alfred O. Hero III

Many developments have recently been made in mining dynamic networks; however, effective visualization of dynamic networks remains a significant challenge. Dynamic networks are typically visualized via a sequence of static graph layouts. In addition to providing a visual representation of the network topology at each time step, the sequence should preserve the “mental map” between layouts of consecutive time steps to allow a human to interpret the temporal evolution of the network and gain valuable insights that are difficult to convey by summary statistics alone. We propose two regularized layout algorithms for visualizing dynamic networks, namely dynamic multidimensional scaling (DMDS) and dynamic graph Laplacian layout (DGLL). These algorithms discourage node positions from moving drastically between time steps and encourage nodes to be positioned near other members of their group. We apply the proposed algorithms on several data sets to illustrate the benefit of the regularizers for producing interpretable visualizations.

K. S. Xu, M. Kliger, and A. O. Hero III. Visualizing the temporal evolution of dynamic networks. In Proc. 9th Workshop on Mining and Learning with Graphs, 2011. (.pdf)

(.pdf)

The animations require a web browser that supports SVG animation with SMIL. The following browsers are capable of displaying the animations:

• Firefox (version 4.0): Animation will display correctly, but cannot be paused. Firefox versions 3.x and lower have native SVG support but no support for SMIL animation.
• Google Chrome (version 8.0 or higher): Animation will display correctly, but cannot be paused.
• Safari (version 5.0 or higher): Animation will display correctly, but cannot be paused.
• Opera (version 10.5 or higher): Animation will display correctly, but cannot be paused.
• Internet Explorer (versions 6.0-8.0): Adobe SVG Viewer must be installed. Full functionality of the animation, including pausing, is available. Internet Explorer 9.0 has native SVG support but does not support SMIL animation; furthermore, it has compatibility issues with Adobe SVG Viewer.

The animations were created using PajekToSvgAnim, with some manual editing afterwards (for example, PajekToSvgAnimdoes not support node colors changing over time).

• DGLL layouts with both regularizers View animation (3.3 MB)
• DGLL layouts with only temporal regularization View animation (3.3 MB)
• DGLL layouts with only group regularization View animation (3.3 MB)
• DGLL layouts with no regularization View animation (3.3 MB)

• DMDS layouts with both regularizers View animation (0.5 MB)
• DMDS layouts with only temporal regularization View animation (0.5 MB)
• DMDS layouts with only group regularization View animation (0.5 MB)
• DMDS layouts with no regularization View animation (0.5 MB)

For comparison, we created an anchored Kamada-Kawai layout in SoNIA (requires Flash, 0.3 MB).

• DMDS layouts with both regularizers View animation (10.4 MB, allow time to load!)