what-when-how
In Depth Tutorials and Information
k
. Denoting by
ik
(
t
),
sk
(
t
), and
rk
(
t
), respectively, the densities of ignorants, spread-
ers, and stiflers and then connectivity
k
, with
ik
(
t
)+
sk
(
t
)+
rk
(
t
) = 1, respectively, the
rumor model can be formed as
di
( )
t
∑
k P k s
'
( ')
( )
,
t
k
= −
λ
ki
( )
t
k
'
k
dt
k
k
'
ds
( )
t
+
∑
k P k s
'
( ')
( )
t
∑
k P k
'
( ')[
s
( )
t
r
( )]
,
t
k
k
'
k
'
k
'
=
λ
ki
( )
t
−
α
ks
( )
t
(3.3)
k
k
dt
k
k
k
'
k
'
dr t
dt
( )
k P k
'
( ')[
s
( )
t
+
r
( )]
t
∑
k
=
α
k
'
k
'
ks
( )
t
k
k
k
'
where
P
(
k
) is the connectivity distribution of the nodes, and
Σ
k
' ( ') ( ) /
is the probability that any given node points to a spreader. Furthermore, D.H.
Zanette [13] found that the rumor model exhibits critical behavior at a finite ran-
domness of the underlying small-world network and studied the transition occur-
ring between regimes where the rumor “dies” in a small neighborhood of its origin.
He [17] studied the dynamics of an epidemic-like model for the spread of a rumor
on a small-world network and found that this model exhibits a transition between
regimes of localization and propagation at a finite value of the network random-
ness. Zonghua Liu et al. [14] investigated infection dynamics by using a three-
state epidemiological model that does not involve the mechanism of self-recovery,
and found that there is a substantial fraction of nodes that can never be infected,
and heterogeneous networks are relatively more robust against spreads of infec-
tion as compared to homogeneous networks. Yamir Moreno et al. [15] studied the
dynamics of the epidemic spreading processes aimed at spontaneous dissemination
of information updates in populations with complex connectivity patterns, and
analyzed the behavior of several global parameters, such as reliability, efficiency,
and load. Yamir Moreno et al. [16] studied the spreading process in detail for ran-
dom scale-free networks, and the result shows that the model could be applied
in replicated database maintenance, peer-to-peer communication networks, and
social spreading phenomena.
k P k s
t
k
'
k
'
3.2 UserBehaviorsintheInformation
PropagationProcess
User behaviors in the information propagation process in online social networks
usually include posting a blog article or picture; reading, commenting on, and
recommending other users' posts, etc. hese multiple user behaviors describe
the details of how the information appears and spreads among online social
