Laplacians is a package containing graph algorithms, with an emphasis on tasks related to spectral and algebraic graph theory. It contains (and will contain more) code for solving systems of linear equations in graph Laplacians, low stretch spanning trees, sparsifiation, clustering, local clustering, and optimization on graphs.
All graphs are represented by sparse adjacency matrices. This is both for speed, and because our main concerns are algebraic tasks. It does not handle dynamic graphs. It would be very slow to implement dynamic graphs this way.
The documentation may be found by clicking on one of the "docs" links above.
To get the current version of the master branch, run
pkg> add Laplacians#master
Change: minor bug fix for spectral graph drawing.
Verified compatibility with Julia 1.2.
harmonic_interpto interpolate harmonic functions on graphs. This is the fundamental routine used in Label Propagation / Semi-Supervised Learning on Graphs.
readIJV. It is a little more robust.
maxflowso that it now returns a flow and cut as a matrix and set.
pcga little more general.
fiedlerfor computing Fiedler vectors and values. That is, the smallest nonzero eigenvalue of the Laplacian.
thickenthat could cause it to loop forever, and cause
chimerato do the same.
plot_graphto plot in 3D.
This version works with Julia version 1.0.0.
ver=Laplacians.V06, as in
a = chimera(2000, 1, ver=Laplacians.V06)
There do seem to be differences in the very low order bits of graphs generated by wted_chimera with the V06 option and those generated in Julia V0.6. Not sure why.
The old generator is obtained by using the
RandomV06 package for Julia.
Changed the names of many functions to bring closer to the Julia standard naming scheme. New names are empty_graph, path_graph, ring_graph, complete_graph, generalized_ring, rand_gen_ring, product_graph, join_graphs, two_lift ... Set deprecation warnings for the old names.
lex.jl to the directory
buggy, as on further testing we found bugs in it.
dropped wGrid3, as it produced a 4d grid so probably wasn't being used anyway. Dropped wGrid2 also.
This is the first version that is compatible with Julia 0.7. Other changes:
Fixed two bugs: one in shortestPaths, and one that prevented passing some parameters to approxchol_sddm. Improved the documentation for solving linear equations.
Fixed a bug in
approxchol_sddm that caused it to be slow.
This version is compatible with Julia 0.6. It will not work with Julia 0.5.X.
approxchol_sddm, a wrapper of
approxchol_lapthat solves SDDM systems.
This is the current version. It is what you retrieve when you run
sparsify, an implementation of sparsification by effective resistance sampling, following Spielman and Srivastava.
conditionNumberfor checking how well one graph approximates another.
approxchol_lap. Made improvements in this solver.
gtimeoutwhen calling Matlab to use icc, CMG, or LAMG.
edgeElimLap- a fast Laplacian solver.
Versions 0.0.3 and 0.1.0 are the same. These versions works with Julia 0.5.
Warning: the behavior of chimera and wtedChimera differs between Julia 0.4 and Julia 0.5 because randperm acts differently in these.
This is the version that works with Julia 0.4. It was captured right before the upgrade to Julia 0.5
The development of this package has been supported in part by the National Science Foundation Award CCF-1562041 and by the Office of Naval Research Award N00014-16-1-2374.
5 days ago