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the weights matrix associated with G i . M i . is defined according to the relation
strength of two nodes. Similarly, the hidden relation can be represented by G'.(V,.
E') and its weight M' . here are two major constraints:
he bond between intracommunity nodes needs to be strong and more
important as well.
Simultaneously, the connection between intercommunity nodes has to be as
weak as possible.
If the weight on the edge is set to be . 1 whenever a relation is made between nodes,
the relation between the labeled nodes can be defined by the following:
M ij = 1 , when nodes i and j have an identical label and 0 otherwise.
When it is uncertain whether or not two objects belong to the similar com-
munity, an alternative M ij formula is provided, and it is defined by M ij = Prob.
( x i and x j belongtothesamecommunity ). Finally, after a series of mathematical
computations, the extracted relation formula was found and can be identified
as
=
M
A M
ext
i
ii
where i can be any value between 1 and 4 and A = [ a 1 ,. a 2 ,.…,. an ] T .
We all know that multiple social networks are composed of complicated, inter-
connected, and multiple graphs, which means that a huge amount of data need
to be gathered. It is a very tough task since the social network is dynamic, and
a user in such a network has a multiple relations with others. However, this net-
work represents the life we are living (reality), so developing multinetwork mining
algorithms based on users' example queries is a suitable approach to solving the
problem.
From the network analysis, a weighted matrix was derived, which is a grouping
of various existing networks. It is important to figure out that derivation, since it
allows one to understand the hidden network even though the ideas behind it are
complex.
It is important to realize that there are multiple and various social networks,
and the blend of such multirelational network may create significant new relation-
ships, which may be useful for users. Moreover, it is important to emphasize that
the new approach to social network and community mining was based on multi-
network and query-based analysis in contrast to the long-established and incom-
plete single-network study. Indeed, we are living in a social network where there
are several relations between users and objects, so the new approach needs to match
this reality. One can say that the query-based relation extraction and community
mining will be a tool applied to many network issues and will definitely lead to new
applications in social network analysis.
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