Currently, eigenspaces of graphs are computed by constructing the adjacency matrix, then converting to a matrix over RDF, and finally computing the eigenspaces of this matrix. When the graph has integer eigenvalues of high multiplicity, numerical inaccuracy is leading to many one-dimensional eigenspaces for what should be the same eigenvalue.
If you request the adjacency matrix of a graph, it is returned as a matrix over the integers and the eigenspaces of this matrix appear to behave better numerically. At least it works well on a graph with 50 vertices having just three distinct eigenvalues. Compare the output of: graphs.CompleteGraph(3).eigenspaces() (three eigenspaces, wrong) with graphs.CompleteGraph(3).am().eigenspaces() (two eigenspaces, correct) 1. I'm guessing the conversion to RDF is historical. I'll make a ticket and improve the situation unless there is an explanation I'm missing. 2. Similarly the spectrum() method for graphs returns RDF, while integer eigenvalues of the adjacency matrix come back as rationals, and non-rational eigenvalues are algebraic numbers. 3. For an undirected graph, the adjacency matrix is symmetric, so the distinction between left and right eigenspaces doesn't matter. For directed graphs, would left and right eigenspace methods be useful, or just clutter? One could always build the adjacency matrix and call the specialized versions already in place for matrices. Thoughts? 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 -~----------~----~----~----~------~----~------~--~---
