web_matrix

web_matrix, a MATLAB code which stores sample matrices describing a web page network. These matrices are typically very sparse, and the examples here are stored using the sparse triplet (ST) format. They can be used to demonstrate pagerank and other graph algorithms.

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

web_matrix is available in a MATLAB version.

Related Data and Programs:

web_matrix_test

arpack_test, a MATLAB code which computes eigenvalues and eigenvectors of large sparse matrices, accessible via the built-in eigs() function;

jordan_matrix, a MATLAB code which returns a random matrix in Jordan canonical form.

levenshtein_matrix, a MATLAB code which returns the Levenshtein distance matrix defined by two strings.

monopoly_matrix, a MATLAB code which computes the adjacency and transition matrices for the game of Monopoly.

pagerank, a MATLAB code which illustrates the eigenvalue (power method) and surfer (Markov chain) approaches to ranking web pages.

plasma_matrix, a MATLAB code which sets up a matrix associated with a problem in plasma physics.

power_method, a MATLAB code which carries out the power method for finding a dominant eigenvalue and its eigenvector.

risk_matrix, a MATLAB code which computes the transition and adjacency matrix for the game of RISK.

snakes_matrix, a MATLAB code which computes the transition matrix for Snakes and Ladders.

sparse_test, a MATLAB code which illustrates the use of sparse matrix utilities;

st, a data directory which illustrates the sparse triplet (ST) format for storing sparse matrices.

st_io, a MATLAB code which reads and writes matrices stored in the sparse triplet (ST) format.

test_matrix, a MATLAB code which defines test matrices for which the condition number, determinant, eigenvalues, eigenvectors, inverse, null vectors, P*L*U factorization or linear system solution are known. Examples include the Fibonacci, Hilbert, Redheffer, Vandermonde, Wathen and Wilkinson matrices.

wathen_matrix, a MATLAB code which compares storage schemes (full, banded, sparse triplet, sparse) and solution strategies (A\x, linpack, conjugate gradient (CG)) for linear systems involving the Wathen matrix, which can arise when solving a problem using the finite element method (FEM).

Reference:

1. John MacCormick,
   Nine Algorithms That Changed the Future: The Ingenious Ideas that Drive Today's Computers,
   Princeton University Press,
   ISBN-13: 978-0691158198.
2. Cleve Moler,
   Experiments with Matlab,
   Chapter 7: Google PageRank
   https://www.mathworks.com/moler/exm/chapters/pagerank.pdf
3. Xindong Wu, Vipin Kumar, J Ross Quinlan, Joydeep Ghosh, Qiang Yang, Hiroshi Motoda, Geoffrey McLachlan, Angus Ng, Bing Lu, Philip Yu, Zhi-Hua Zhou, Michael Steinbach, David Hand, Dan Steinberg,
   Top 10 algorithms in data mining,
   Knowledge and Information Systems,
   Volume 14, Number 1, January 2008, pages 1-37.

Source Code:

• harvard_st.m, defines the "Harvard" matrix with 500 nodes and 2636 links.
• incidence_to_transition.m, computes the transition matrix associated with an incidence matrix.
• large_st.m, defines the "large" matrix with 1458 nodes and 3546 links.
• mac1_st.m, defines the "MacCormick #1" matrix with 5 nodes and 5 links.
• mac2_st.m, defines the "MacCormick #2" matrix with 16 nodes and 27 links.
• medium_st.m, defines the "medium" matrix with 316 nodes and 431 links.
• moler_st.m, defines the "Moler" matrix with 6 nodes and 10 links.
• power_rank.m, uses the power method to perform a simple ranking of web page nodes.
• sauer_st.m, defines the "sauer" matrix with 15 nodes and 34 links.
• six_st.m, defines the "six" matrix with 6 nodes and 9 links.
• small_st.m, defines the "small" matrix with 93 nodes and 196 links.
• tiny_st.m, defines the "tiny" matrix with 5 nodes and 8 links.