Visual Computing

University of Konstanz
IEEE Transactions on Visualization and Computer Graphics

Probabilistic Graph Layout for Uncertain Network Visualization

C. Schulz, A. Nocaj, J. Görtler, O. Deussen, U. Brandes, D. Weiskopf
Teaser of Probabilistic Graph Layout for Uncertain Network Visualization


Paper (.pdf, 17.1 MB)


We present a novel uncertain network visualization technique based on node-link diagrams. Nodes expand spatially in our probabilistic graph layout, depending on the underlying probability distributions of edges. The visualization is created by computing a two-dimensional graph embedding that combines samples from the probabilistic graph. A Monte Carlo process is used to decompose a probabilistic graph into its possible instances and to continue with our graph layout technique. Splatting and edge bundling are used to visualize point clouds and network topology. The results provide insights into probability distributions for the entire network—not only for individual nodes and edges. We validate our approach using three data sets that represent a wide range of network types: synthetic data, protein–protein interactions from the STRING database, and travel times extracted from Google Maps. Our approach reveals general limitations of the force-directed layout and allows the user to recognize that some nodes of the graph are at a specific position just by chance.


  author     = {C. Schulz and A. Nocaj and J. Görtler and O. Deussen and U. Brandes and D. Weiskopf},
  doi        = {10.1109/TVCG.2016.2598919},
  issn       = {1077-2626},
  journal    = {IEEE Transactions on Visualization and Computer Graphics},
  keywords   = {Monte Carlo methods;data visualisation;diagrams;graph theory;network theory (graphs);statistical distributions;Monte Carlo process;edge probability distribution;node-link diagram;probabilistic graph decomposition;probabilistic graph layout;protein-protein interaction;synthetic data;uncertain network visualization;Data visualization;Layout;Probabilistic logic;Probability density function;Probability distribution;Uncertainty;Visualization;Monte Carlo method;Uncertainty visualization;edge bundling;graph layout;graph visualization},
  month      = {jan},
  number     = {1},
  pages      = {531--540},
  title      = {Probabilistic Graph Layout for Uncertain Network Visualization},
  volume     = {23},
  year       = {2017},
  url        = {},