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Graph Drawing of Matrices
AT&T Labs Research
Project Description:
In mathematics, a matrix is a rectangular table of elements (or entries), which may be numbers or, more generally, any abstract quantities that can be added and multiplied. A sparse matrix is a type of matrix that while vast and multi-dimensional, consists mostly of empty space or zeros. They occur often enough to have a place in our work on science, mathematics and information theory.

The two examples shown here are part of a vast gallery of graphs generated from 1890 sparse matrices in the University of Florida Sparse Matrix collection. Each of these sparse matrices is viewed as the adjacency matrix of an undirected graph, and is laid out by a multilevel graph drawing algorithm. If the graph is disconnected, then the largest connected component is drawn. The largest graph has 8863287 vertices and 44185251 edges. A simple coloring scheme is used: if the matrix has real entries, coloring is based on the entry value, otherwise it is based on the edge length.

Through this exercise the authors hope to have a better understanding on the type of structures studyed by people doing large scale computation.

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Manuel Lima |