Analyzing and Securing Social Networks

182 Analyzing and Securing Social Networks

the ow of information through the graph. We refer to these as class-weighted graph metrics, and

alter their equations as follows:

wCC

jk jk jk Cj Ck

dd

i

i

ii

=

∈∈=

−

|{(, )| ,,(, ),() ()}|

()

NE

1

−−

∈∈≠

−

|{(, )| ,,(, ),() ()}|

()

jk jk jk Cj Ck

dd

i

ii

NE

1

(16.3)

and

wDC

cc

i

ii

=

−

−

NN

V

()

()

1

(16.4)

where



i

c

()

are the neighbors of n

i

who share the same class as n

i

, and



i

c

()

are the neighbors

of n

i

who are in the opposite class of n

i

.

It is important to note that we are not attempting to determine links that represent real-world

relationships. Instead, we are attempting to model the ow of information or preferences through ...