How to calculate edge betweenness centrality in Big Data with example?

Let us take an example,

We need to find for all combinations of edges 

For edge (1,2)

Does edge (3,5) comes while traversing from 1 to 2 ? No 

so the numerator is 0

The shortest path between 1 to 2 is only 1

so the denominator is 1

= 0/1 = 0 

Similarly,

For edge (1,3) = 0/1 = 0

For edge (1,4 )

Does edge (3,5) comes while traversing from 1 to 4 ? No 

so the numerator is 0

The shortest path between 1 to 4 is 2 [1-2-4, 1-3-4]

so the denominator is 2

= 0/2 = 0 

For edge (1,5)

Does edge (3,5) comes while traversing from 1 to 5 ? Yes

so the numerator is 1

The shortest path between 1 to 5 is 1 [1-3-5]

so the denominator is 2

= 1/2 = 0.5

Similarly,

For edge (1,6)

1/3 =  0.33

For edge (2,3)

0/2 = 0

For edge (2,4)

0/1 =0 

For edge (2,5)

1/3 = 0.33 

For edge (2,6)

0/1 =0

For edge (3,4)

0/1 =0

For edge (3,5)

1/1 = 1

For edge (3,6)

1/2 = 0.5 

For edge (4,5)

1/2 = 0.5 

For edge (4,6)

0/1 = 0

For edge (5,6 )

0/1 = 0

Finally summing all the values, we get 

0.5 + 0.33 +0.33 + 1 + 0.5 + 0.5 = 2.5 + 0.66 = 3.16

More Engineering Blogs