Router Graphs

 Here is a router graph using data from Tom. The vertices are routers, and the edges are interconnections. This graph has 81 vertices 114 edges diameter of this router graph is 6 maximum degree 21. Here are several layouts of the above graph using different algorithms.    Ideas of the algorithms:
• Find the BFS tree rooted at the vertex with largest degree.
• Assign the coordinates of children around the parent (with respect to the BFS tree) with Gaussian distribution.
• The parameter sigma in Gaussian distribution decreases as the distance from root grows.
• Apply a transformation, which moves the children vertices away from their great parent vertex.
The details of the algorithms will be included in a new paper "graph visualizations" (in preparation).

Remarks on the pictures on the right.
• The second figure is derived by using the same algorithms except that the children vertices are spreaded evenly around the parent.

• The Third figure is based on the second figure with additional application of barycenter algorithms several times.

• The fourth figure is obtained by a "expansion" algorithm. Here two forces are used. One force is the "spring" factor having value 1 assigned to each edge. The other force is the "flux" factor having the same value assigned to each vertex.