SSDE: Fast Graph Drawing Using Sampled Spectral Distance Embedding

  • Çivril A
  • Magdon-Ismail M
  • Bocek-Rivele E
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We present a fast spectral graph drawing algorithm for draw-ing undirected connected graphs. Multi-Dimensional Scaling is a quadratic spectral algorithm, which approximates the real distances of the nodes in the final drawing with their graph theoretical dis-tances. We build from this idea to develop a linear spectral graph drawing algorithm SSDE. We reduce the space and time complexity of the spectral decomposition by approximating the distance ma-trix with the product of three smaller matrices, which are formed by sampling rows and columns of the distance matrix. The main advantages of our algorithm are that it is very fast and it gives aes-thetically pleasing results, when compared to other spectral graph drawing algorithms. The runtime for typical 10 5 node graphs is about one second and for 10 6 node graphs about ten seconds.

Author-supplied keywords

  • approximate matrix reconstruction
  • eigenvector
  • power iteration
  • random sampling
  • singular value decomposition

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  • Ali Çivril

  • Malik Magdon-Ismail

  • Eli Bocek-Rivele

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