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networks. This conclusion means that the leak of private information or pictures
causes serious problem on the online social networks (Dan 2011a , b ).
User Generated Content (UGC) is currently popular for exchanging information
amongst Internet users. Orita ( 2008 ) pointed out that users in Japan prefer to remain
anonymous although they make good use of such UGC. Once the personal infor-
mation of users is open on the Internet, it diffuses on the network, all users in the
community can access the information, and it becomes too difficult to go back to the
state of anonymity.
Even if we include the effect of deletion, which is linear in time, we could not
stop the diffusion of personal information throught social networks on the Internet.
As is shown in the simulate on later, the diffusion of information progresses at the
rate of exponential growth. Thus, deletion is ineffective as we completely delete all
references to the information in digital format.
3.3.2 Dissipative Effect
There are at least two approaches to dissipative operations concerning the informa-
tion diffusion process. One is to eliminate the main hub in a scale-free network, the
other is to decrease the diffusion speed. We can realize the latter operation through
the reduction of the probability to diffuse information on the network. It is proposed
in this chapter that the dissipative operations are effective in protection of confi-
dential information.
For the protection of personal information, it should be pointed out that there are
three other options. For technical reasons, we should use cryptography to store and
communicate personal information. Secondly, from the viewpoint of the law
system, we should develop and manage appropriate measures concerning the
protection of personal information. Lastly but most importantly, we need to educate
or enlighten users.
3.4 Mathematical Modeling
3.4.1 Set Theoretic Model
A social network (Newman 2010 ) can be modeled using mathematics, that is, a set of
points (also called vertices or nodes ) connected by lines (also called edges or links ).
Let us consider a social network according to the usual method by Wasserman
and Faust ( 1994 ). U is defined below as a set of users in the social network
U
¼f
u 1 ;
u 2 ; ...;
u n g;
(3.1)
where n is the number of users in the social network. The elements of U are points
of a graph in the geometrical view.
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