Pseudo-Random Graph

The drawings show a pseudo-random graph with eight cluster of 50 nodes. The probability of an edge {u, v} is

• 1 if u and v belong to the same of the first four clusters,

• 0.5 if u and v belong to the same of the second four clusters,

• 0.2 if u and v belong to different of the first four clusters,

• 0.05 if u and v belong to different of the second four clusters, and

• 0.1 if u belongs to one of the first and v belongs to one of the second four clusters.

Both LinLog energy models reveal the clusters, but their drawings differ because the degrees of the nodes are nonuniform. The node-repulsion LinLog drawing places the first four clusters more closely than the second four clusters, which reflects that node-normalized cuts between the first four clusters are higher than between the second four clusters. In the edge-repulsion LinLog drawing the distances between all clusters are similar, which reflects that the edge-normalized cuts between all pairs of clusters are similar.

Fruchterman-Reingold model		Node-repulsion LinLog model		Edge-repulsion LinLog model