Issue No. 05 - Sept.-Oct. (2013 vol. 15)

ISSN: 1521-9615

pp: 42-55

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/MCSE.2012.91

James L. Johnson , Western Washington University

Tom Goldring , US National Security Agency

ABSTRACT

Hodge theory provides a unifying view of the various line, surface, and volume integrals that appear in physics and engineering applications. Hodge theory on graphs develops discrete versions of the differential forms found in the continuous theory and enables a graph decomposition into gradient, solenoidal, and harmonic components. Interpreted via similarity to gradient, curl, and Laplacian operators on vector fields, these components are useful in solving certain ranking and approximations problems that arise naturally in a graph context. This tutorial develops the rudiments of discrete Hodge theory and provides several example applications.

INDEX TERMS

Graph theory, Context awareness, Indexes, Tutorials, Approximation algorithms, Scientific computing, Discrete mathematics,scientific computing, discrete Hodge theory, graph theory, discrete mathematics, simplicial complexes, Hodge decompositions

CITATION

James L. Johnson, Tom Goldring, "Discrete Hodge Theory on Graphs: A Tutorial",

*Computing in Science & Engineering*, vol. 15, no. , pp. 42-55, Sept.-Oct. 2013, doi:10.1109/MCSE.2012.91