web_matrix

web_matrix, an Octave 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.

Languages:

web_matrix is available in a MATLAB version and an Octave version..

Related Data and Programs:

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

levenshtein_matrix, an Octave code which returns the Levenshtein distance matrix defined by two strings.

monopoly_matrix, an Octave code which computes the adjacency and transition matrices for the game of Monopoly.

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

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

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

risk_matrix, an Octave code which computes the transition and adjacency matrix for the game of RISK.

snakes_matrix, an Octave code which computes the transition matrix for Snakes and Ladders.

sparse_test, an Octave code which illustrates the use of sparse matrix utilities;

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

test_matrix, an Octave 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, an Octave 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,
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.