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k-core based Multi-level Graph Visualization for Scale-free Networks

• Seokhee Hong shhong (at) it.usyd.edu.au
  The University of Sydney, Sydney, New South Wales, Australia
• An Nguyen angu5603 (at) uni.sydney.edu.au
  University of Sydney

Abstract

We present a new multi-level graph drawing algorithm based on the {\\it k-core} coarsening, a well-known cohesive subgroup analysis method in social network analysis. \ The {\\it k-core} of a graph is also known as the {\\em degeneracy} in graph theory, and can be computed in linear time. \ Our {\\it k}-core based multi-level algorithm also includes a new {\\em concentric circle placement} and a variation of force-directed layout to display the structure of graphs effectively. \ \ Experiments with real-world networks suggest that our algorithm performs well for visualization of large and complex {\\em scale-free} networks, with a power-law degree distribution, a short diameter and a high clustering coefficient. \ Comparison with other multi-level algorithms shows that our method is fast and effective, in particular performs better than Walshaw~\\cite{walshaw2003multilevel} and FM\\textsuperscript{3}~\\cite{hachul2005drawing}.