On Jun 8, 7:47 pm, Jason Grout <jason-s...@creativetrax.com> wrote: > I've never had to use the left eigenvectors of a graph.
And I've never needed a directed graph so my matrices are always symmetric. (Just kidding.) ;-) The above is now: http://trac.sagemath.org/sage_trac/ticket/6258 A related question: matrices and graphs have eigenspaces() methods, but matrices have eigenvalues() and graphs have spectrum(). The spectrum() method seems identical in the style of its output to the eigenvalues() method - a list of eigenvalues repeated according to multiplicity. Furthermore, in algebraic graph theory the term "spectrum" is closely tied to both the values of the eigenvalues and their multiplicities. For example, graphs.HoffmanSingletonGraph() has 50 eigenvalues but just three are distinct. The usual shorthand is to list the eigenvalues with their multiplicities as an exponent - for the Hoffman- Singleton graph this would look like 7^1 2^28 (-3)^21 Yes, you can count the multiple eigenvalues, or write a routine to do it for you, but I think this is something that should be built into Sage. So a proposal for graphs: 1. Add a new eigenvalues() method for a graph, identical to the current spectrum(), more in line with the use for matrices. 2. Have spectrum() return something like a list of pairs (e_i, m_i) with m_i being the multiplicity of eigenvalue e_i, more in line with expectations for the term. For example, "Algebraic Graph Theory" (Godsil and Royle) says the spectrum is the "list of the eigenvalues together with their multiplicities." Biggs' "Algebraic Graph Theory" says the spectrum "is the set of numbers which are eigenvalues, together with their multiplicities." Rob --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
