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For example, user a and user b have forwarded f, and the user a also forwarded
user e.
N
N
is the number of a forwarded f,
is the number of b forwarded f,
bf
af
BR b
are important degree. We can
make conclusion as following (I) if the number of a forwarded f is more i.e.
N
is the number of a forwarded e.
BR a
and
()
()
ae
. It is suggest that user a make a larger contribution to f. (II) if user a is
more important than b i.e.
NN
>
af
bf
.The user a will make a larger contribution
to f. (III) The user a forwarded e and f, but if
BR a
()
>
BR b
()
, it suggest that user a make a
NN
>
af
ae
larger contribution to f.
These three conclusions obtained above are consistent with the idea of PageRank
algorithm; the interactive behavior can change the node influence. Forwarding can be
as the voting behavior, the more number of forwarding equivalent to more votes, "the
greater support to other users", such as the above conclusions (I) (III); if it is an
important vote, the "support" will be greater, likes the above conclusion (II). Unlike the
original PageRank algorithm, the node "contribution" in this paper is not the average
distribution, in the conclusion (III) have illustrated this point. Distribution of the
"contribution" is related to the number of forward or comments; the more forward the
more "contribution". For the general case, If the relationship of forward or comment
between nodes v and u is existed, the node v forward node u, then use the following
formula to express the v to u "contribution" ratio:
N
(8)
p
=
vu
vu
N
vx
xOv
∈
()
The
stand for number of
v
forward u,
Ov
is the set of
v
forwards,
is
v
N
N
()
vu
vx
forwards others, where
v
p
represents the probability of v forward u.
The core idea of PageRank is to calculating the PR value of each node value
according to the number of back links, uniform "flow" to all nodes. Each node's PR
value is the total of "contribution" of node's PR value. We borrowed this idea. Then we
revised the problems of "contribution" average distribution, and put forward the
calculating formula evaluation node behavior influence:
BR u
() (1
=− ×
d
)
BR u
()
+
d
p
BR v
()
(9)
vu
vIu
∈
()
This is an iterative formula. The initial value of
BR
is related to
AR
refer to formula
(6), and where
Iu
is set of pointed to
u
in
directed graph. The value of d is 0.85.The formula (9) combines the characteristics of
online social network and its application background.
The value of BR represents the influence of behavior; the calculation process of BR
is following:
Calculation of the value of BR
Get data set G=(V,E),where V is users set, E is relationship set, initial AR,
BR, N
vu
, P
vu
, d, ε, σ
p
()
is distribution probability, where
vu
