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Lake Arrowhead Coauthor Graph Photos 1

Posted by Cleve Moler,

Nick Trefethen has framed the original flip chart that I described in my Lake Arrowhead Coauthor Graph blog earlier this week and has it on the wall of his office at Oxford University. His colleage Nick Hale has taken these photos. (The faded name in the cell at the lower left just northwest of mine is Tony Chan.)

Let's repeat John Gilbert's social network analysis of this data.

load housegraph
r = symrcm(A(2:end,2:end));
prcm = [1 r+1];
drawit


Get the MATLAB code

Published with MATLAB® R2013b

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Javier Fernández replied on : 1 of 1
Looking at the top left of the flip chart, Fierro has made me realize that taking away the diagonal Ad=A-speye(size(A)); pmdd = amd(Ad); spy(Ad(pmdd,pmdd)) find(pmd-pmdd) ans = Empty matrix: 1-by-0 it still looks almost like an arrowhead, but rank(full(A)) ans = 101 rank(full(Ad)) ans = 97 so he is trying to help both with the arrowhead and the Ax=b annotation. Also, if the diagonal were removed, entries in A^n would be paths of length==n, not <=n, changing (spoiling?) the meaning of depth and diameter. Curiously, computation of tree depth p=4 from Golub is not affected, meaning Golub has a length-4 path to everyone (in fact, length-3 to everyone but 3), and diameter changes only from p=7 to 8 (I think it would remain 7 if an edge existed among Ipsen's coauthors). Back to Ax=b and trying rref, I think I understand why a repeated coauthor list gets its column off jb and annotated with the first index, but I'm still studying the third case. I find it fascinating that the rref is unique, even moving Golub to the end (only changes index), even interchanging Kahan-Davis (no change at all). Thanks for the explanation on how prcm was obtained. Now I realize I didn't understand the hint in the comment for symrcm, which I thought to be soothing for the untaught :-). Kaufman-Ammar are interchanged in prcm-symrcm, but that doesn't affect global bandwidth. Looking at the top right and center bottom of the chart, Edelman and Stewart have links outside the graph. There are also two outward links near the top left. Maybe the flipchart is folded on the sides, or annotated in the back... I think somebody wrote down Householder's name as a token of respect (can't guess who from handwriting). 'Pete' wrote an article and preface, and I still didn't notice. It was looking for edges to Householder (Gragg, Stewart, Varga, Wilkinson) using AMS MathSciNet (learned about it in the Wikipedia entry for Golub), when I realized Wilkinson could not be there (also looked for Henrici, also found out what Senior Wrangler means.) I should have noticed earlier, you recently told us. That article and this other made me remember about your "Case closed. Project grade: A." using invhilb. I think it relates to the '61 paper mentioned there. Cleve, I'm still trying to decide if I should cheer up or frown upon the Kurzentrum and the modest quantities stories. It's always you who makes us learn about them. I'd say the frame has been placed on what seems a wooden surface, perfectly perpendicular to the camera, to make a better shot. Thanks to Nick Hale's (determined and) successful efforts to capture the additional closeups, most of the names can be located (around 3/4). It's a shame the bottom caption is so small. There seems to be 6 or 7 lines of text. Maybe it just tells the story of the graph, like runme.m. Does it explain the Ax=b annotation linked to Wilkinson? Or the outward links?