Information Technology Reference
In-Depth Information
Fig. 3.3
The result of diffusion process in a trial of the simulation. The population who knows the
information or are infected increases 60 at the first percolation, up to 89 at the next percolation, and
so on. We can see the saturation point, that is, the information is diffused by all people until the
1023rd time step
We can calculate the number of links which the user
u
i
∈
U
has, as the following
quantity:
1
X
;
024
a
ij
(3.20)
j¼
1
As the nature of preference selection method,
u
i
is likely to have more links if
i
is
small (Kullmann and Kert´sz
2001
).
Next, we gave the initial condition to the simulation program. Take one user
u
i
∈
U
who has known a piece of information or been infected by something at first.
Then the users who have the links to
u
i
can reach the information at the next time
step. Therefore the information diffuses through percolation. All we want to know
is how many people know a piece of information or are infected at each time step,
because we can see the diffusion process and the speed of information diffusion on
the networks. The program of the simulation makes a loop percolation as time
increased at time steps. Figure
3.3
indicates the result of a trial of the simulation. It
can be proved in general that the information diffused to all the people until the
number of time steps is equal to the number of elements of
U
, if the initial user of
information diffusion is the main hub of the network.
