Social Balance Theory

relation, and 0 for no-relation. From the matrix, the possible triads can be determined to
be balance or not, and we can also determine the balance index of the network.

Table 3

The possible triad combinations of a group of agents (N) = 4

As an example, we randomize the initial states represented by initial adjacency
matrix and measure the balance index from the initial interpersonal network. From the
adjacency matrix we construct a string describing the edges of each interconnection
(dyadic relations) explained in table 2 (see table 5). Mutation is played randomly among
the edges string from every possible formed relation. Based upon the Heider’s triad
balance theory, an individual will try to balance every relation that it has (Heider, 1946)
then any mutation or the change of sentiment relation sign will occur by the terms, i.e.:

Pr[R_i =0→R_i =1|R_i =0→R_i =-1]≈1               (5)

ij                          ij                   ij                          ij

Pr[R_i =1→R_i =0|R_i =-1→R_i =0]=0              (6)

ij                         ij                    ij                             ij

Table 4

Adjacency matrix among individuals in a
group of 4 members

Table 5

The Edges String (dyadic relation) to which we do
change of sentiment signs or mutation.

1 ÷ 2

1 ÷ 3

1 ÷ 4

2 ÷ 3

2 ÷ 4

3 ÷ 4

The probability of string mutation from 0 to 1 or -1 is very big since people in a group
are encouraged to meet and know each other. In the other hand, the probability of string

<<   <   3   4   5   6   7   8   9   >   >>