SSDE: Fast Graph Drawing Using Sampled Spectral Distance Embedding

Abstract

We present a fast spectral graph drawing algorithm for drawing 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 distances. 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 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 10 5 node graphs is about one second and for 10 6 node graphs about ten seconds