49  Homework IV: Matrix Operations

Consider the graphs shown in Figure 51.1:

(a) Studying with network.

(b) Going out with network.

Figure 49.1: Two graphs representing two different set of network ties between the same people.

  1. Write down the adjacency matrix corresponding to each network:

Table 49.1: Two graphs representing two different set of network ties between the same people.

(a) Studying with network.
A B C D E F G H
A -
B -
C -
D -
E -
F -
G -
H -
(b) Going out with network.
A B C D E F G H
A -
B -
C -
D -
E -
F -
G -
H -
  1. Write down the matrix sum and the element-wise product of the adjacency matrices you filled out above:

Table 49.2: The sum and element-wise product of the adjacency matrices representing two different set of network ties between the same people.

(a) Matrix Sum.
A B C D E F G H
A -
B -
C -
D -
E -
F -
G -
H -
(b) Element-Wise Product.
A B C D E F G H
A -
B -
C -
D -
E -
F -
G -
H -

  1. Write the down the dyads that are connected via multiplex ties (dyads sharing more than one relationship at a time):



  2. Write the down the dyads that are connected via uniplex ties (dyads sharing only one relationship at a time):



Consider the graphs shown in Figure 49.2:

Figure 49.2: A directed graph.

  1. Fill out the four matrices below:

Table 49.3: Some Matrices Derived From a Directed Graph.

(a) Adjacency Matrix (A).
A B C D E F G
A -
B -
C -
D -
E -
F -
G -
(b) Adjacency Matrix Transpose (A’).
A B C D E F G
A -
B -
C -
D -
E -
F -
G -
(c) One Minus Transpose (1 - A’)
A B C D E F G
A -
B -
C -
D -
E -
F -
G -
(d) Mutual Dyads Matrix (A * A’).
A B C D E F G
A -
B -
C -
D -
E -
F -
G -
(e) Asymmetric Dyads Matrix (A * 1-A’)
A B C D E F G
A -
B -
C -
D -
E -
F -
G -

  1. How many mutual dyads in the graph?





  2. How many asymmetric dyads in the graph?





  3. What is the graph reciprocity?