Drawing Power Law Graphs

It has been noted that many realistic graphs have a power law degree distribution and exhibit the small world phenomenon. We present drawing methods influenced by recent developments in the modeling of such graphs. Our main approach is to partition the edge set of a graph into “local” edges and “global” edges, and to use a force-directed method that emphasizes the local edges. We show that our drawing method works well for graphs that contain underlying geometric graphs augmented with random edges, and demonstrate the method on a few examples. We define edges to be local or global depending on the size of the maximum short flow between the edge’s endpoints. Here, a short flow, or alternatively an -short flow, is one composed of paths whose length is at most some constant . We present fast approximation algorithms for the maximum short flow problem, and for testing whether a short flow of a certain size exists between given vertices. Using these algorithms, we give a f...

• Type: Conference
• Year: 2004
• Where: GD
• Authors: Reid Andersen, Fan R. K. Chung, Lincoln Lu
• Keywords: GD 2004, Law Degree Distribution, Power Law Degree, Short flow