Information Diffusion and Dissipative Effect on Social Networks - IT Enabled Services - page 47

3.5.3.1 Complete Networks

A complete network is the network of whose two vertices have an edge. There is no
pair that does not have an edge in the network. When the number of vertices is n , the
network has n ( n

U
is a complete network. Dan ( 2011a ) investigated the mathematical modeling and
computer simulation of diffusion phenomena on social networks for complete
networks.

1)/2 edges. In our notation, a social network U with R ¼ U

3.5.3.2 Random Networks

A random network is one whose vertices have edges at random. Randomness is
assumed for not only uniform distribution, but also any possible function of
distribution. Dan ( 2011b ) has pointed out that the structure of random networks is
similar to that of stochastic networks in diffusion processes.

3.5.3.3 Stochastic Networks

Conversely, for a stochastic network, each edge has a probability value between
zero and one. Each edge mediates the information at the probability that depends on
the edge. One can communicate on the edge at the probability p , otherwise one
cannot communicate on the edge at the probability 1

p . The possibility of
communication depends on the probability p defined for each edge. In the simula-
tion, we use uniform stochastic networks with a constant p for dissipative
operations.

3.5.3.4 Scale-Free Networks

In a scale-free network, the power-law is used for the number of edges. There are
some vertices, which are called hubs , that have comparably large number of edges.
On the other hand, almost all vertices have only a few edges. The graph of the
number of edges indicates the law of power. Scale-free networks were first pro-
posed as small-world networks by Watts and Strogatz ( 1998 ), then Barab´si and
Albert ( 1999 ) have constructed their models for scale-free networks.
It is known that scale-free networks have high cluster coefficients like regular
lattices. However, these networks have small characteristic path lengths like ran-
dom networks.
We use scale-free networks in our simulation.