SSDE: Fast Graph Drawing Using Sampled Spectral Distance Embedding
نویسندگان
چکیده
We present a fast spectral graph drawing algorithm for drawing undirected connected graphs. Classical Multi-Dimensional Scaling yields a quadratictime spectral algorithm, which approximates the real distances of the nodes in the final drawing with their graph theoretical distances. We build from this idea to develop the linear-time spectral graph drawing algorithm SSDE. We reduce the space and time complexity of the spectral decomposition by approximating the distance matrix 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 aesthetically pleasing results, when compared to other spectral graph drawing algorithms. The runtime for typical 105 node graphs is about one second and for 106 node graphs about ten seconds.
منابع مشابه
SDE: Graph Drawing Using Spectral Distance Embedding
We present a novel graph drawing algorithm which uses a spectral decomposition of the distance matrix to approximate the graph theoretical distances. The algorithm preserves symmetry and node densities, i.e., the drawings are aesthetically pleasing. The runtime for typical 20, 000 node graphs ranges from 100 to 150 seconds.
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