Mining Massive Datasets - adjacency matrix, degree matrix, laplacian matrix.

mmds-q3a.R

Q1

  C -- D -- E
 / |    |    | \
A  |    |    |  B
 \ |    |    | /
   F -- G -- H

Write the adjacency matrix A, the degree matrix D, and the Laplacian matrix L. For each, find the sum of all entries and the number of nonzero entries. Then identify the true statement from the list below.

Adjacency Matrix

  A B C D E F G H
A 0 0 1 0 0 1 0 0
B 0 0 0 0 1 0 0 1
C 1 0 0 1 0 1 0 0
D 0 0 1 0 1 0 1 0
E 0 1 0 1 0 0 0 1
F 1 0 1 0 0 0 1 0
G 0 0 0 1 0 1 0 1
H 0 1 0 0 1 0 1 0

Degree Matrix

2,2,3,3,3,3,3,3

Laplacian Matrix

L = D - A

First, fill out diagonal from laplacian matrix down-right on the matrix.
Next, change the sign of remaining values.

   A  B  C  D  E  F  G  H
A  2  0 -1  0  0 -1  0  0
B  0  2  0  0 -1  0  0 -1
C -1  0  3 -1  0 -1  0  0
D  0  0 -1  3 -1  0 -1  0
E  0 -1  0 -1  3  0  0 -1
F  -1 0 -1  0  0  3 -1  0
G  0  0  0 -1  0 -1  3 -1
H  0 -1  0  0 -1  0 -1  3

A has 22 nonzero entries.
D has 8 nonzero entries.
L has 30 nonzero entries.
The sum of the entries of A is 22.