ORIE 4850
Problem Set #4
Due: Thurs. October 8 at 12noon.
(
Note
: for all computations done with matlab, you should hand in the printouts.
*’s
indicate a more difficult problem.)
1.
Consider the example we did in class with two ncliques (where each node in the first
clique had an edge going to its corresponding node in the 2
nd
clique) and the
“reduced” 2node digraph that we analyzed.
a.
Using Matlab, directly compute the eigenvalues for n=2, d=0.15. Don’t use
the reduced digraph here! (Hint: matlab allows you to combine smaller
matrices into larger ones, e.g. if A,B,C,D are nxn matrices then [A,B;C,D] is a
(2n)x(2n) matrix . Also, eye(n) gives an nxn identity matrix which can be
useful.)
b.
**Why doesn’t the 2
nd
eigenvalue from part (a) agree with our result from
class?
c.
Redo part (a) for n=80, d=0.15 and compare to the analytical result from class.
2.
Again consider the example we did in class with two ncliques, where each node in
the first clique had an edge going to its corresponding node in the 2
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 Fall '07
 KOCH
 Matrices, Ring, 1%, Block matrix, corresponding node

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