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Discrete Hodge Theory on Graphs: A Tutorial
Sept.-Oct. 2013 (vol. 15 no. 5)
pp. 42-55
James L. Johnson, Western Washington University
Tom Goldring, US National Security Agency
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 and Engineering, vol. 15, no. 5, pp. 42-55, Sept.-Oct. 2013, doi:10.1109/MCSE.2012.91
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