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James L. Johnson, Tom Goldring, "Discrete Hodge Theory on Graphs: A Tutorial," Computing in Science and Engineering, vol. 15, no. 5, pp. 4255, Sept.Oct., 2013.  
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@article{ 10.1109/MCSE.2012.91, author = {James L. Johnson and Tom Goldring}, title = {Discrete Hodge Theory on Graphs: A Tutorial}, journal ={Computing in Science and Engineering}, volume = {15}, number = {5}, issn = {15219615}, year = {2013}, pages = {4255}, doi = {http://doi.ieeecomputersociety.org/10.1109/MCSE.2012.91}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  MGZN JO  Computing in Science and Engineering TI  Discrete Hodge Theory on Graphs: A Tutorial IS  5 SN  15219615 SP42 EP55 EPD  4255 A1  James L. Johnson, A1  Tom Goldring, PY  2013 KW  Graph theory KW  Context awareness KW  Indexes KW  Tutorials KW  Approximation algorithms KW  Scientific computing KW  Discrete mathematics KW  scientific computing KW  discrete Hodge theory KW  graph theory KW  discrete mathematics KW  simplicial complexes KW  Hodge decompositions VL  15 JA  Computing in Science and Engineering ER   
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/MCSE.2012.91
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. 4255, Sept.Oct. 2013, doi:10.1109/MCSE.2012.91
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