Complex Networks
Our research in complex networks concentrates on analysis of stochastic processes on simple graphs and higher order distributions. Moreover we are interested in visualisation and parallel simulation of complex networks. Recently we finished a new algorithm which uses multi-level gamma-clustering to visualize complex biological networks.
The software and experimental data could be found in the following file DownloadMultiLevelGammaClustering_suppl.zip (ZIP, 973 KB)
To illustrate the different ways of rendering a graph we prepared 5 demonstrations. For all we have used the same settings for the generation of the graph (ConfigModel with gamma = 1.75 and 600 nodes).
Classic Force Directed
Here we used a classical force directed algorithm that is based on a physical model. The edges are interpreted as springs which gives the attraction force. In addition, a so called anti-gravity is applied that provokes a repulsion of all nodes.
Circular Force Directed Using Heuristics
Here the positioning algorithm is equivalent to the previous one. In addition, a 'correction displacement' is calculated to force each node on a circle according to its degree.
UCircular Force Directed with Hierarchical Gamma Clustering Using Heuristics
This rendering is equivalent to the previous one, with the same addition as seen in the third example: With a 'correction displacement' the nodes are forced on circles according to their distance (=number of edges) from the root node (root node not shown here, would be placed in the center).
Force Directed Using Heuristics
In addition to the classical force directed method, here we implemented heuristics as explain in the Lukas Oertle's master thesis. These heuristics are intended to take care of the osciallation observed in the classical algorithm. On the one hand, an internal temperature is lowered slowly so that the nodes will for sure come to a final position. On the other hand, each step a node makes is interpolated with the last 4 steps. In this way opposing movement neutralize each other.
Force Directed with Hierarchical Gamma Clustering Using Heuristics
Again, the positioning algorithm is left mainly untouched except for some constants. Before the actual rendering is started the graph was 'prepared' as explained in our paper 'Hierarchical Gamma Clustering'.