Visualizing Very Large Graphs Using Clustering Neighborhoods

Abstract

This paper presents a method for visualization of large graphs in a two-dimensional space, such as a collection of Web pages. The main contribution here is in the representation change to enable better handling of the data. The idea of the method consists from three major steps: (1) First, we transform a graph into a sparse matrix, where for each vertex in the graph there is one sparse vector in the matrix. Sparse vectors have non-zero components for the vertices that are close to the vertex represented by the vector. (2) Next, we perform hierarchical clustering (eg., hierarchical K-Means) on the set of sparse vectors, resulting in the hierarchy of clusters. (3) In the last step, we map hierarchy of clusters into a two-dimensional space in the way that more similar clusters appear closely on the picture. The effect of the whole procedure is that we assign unique X and Y coordinates to each vertex, in a way those vertices or groups of vertices on several levels of hierarchy that are stronger connected in a graph are place closer in the picture. The method is particular useful for power distributed graphs. We show applications of the method on real-world examples of visualization of institution collaboration graph and cross-sell recommendation graph.