Physics Letters A 376 (2012) 2103–2108
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Physics Letters A
www.elsevier.com/locate/pla
An information diffusion model based on retweeting mechanism
for online social media
Fei Xiong
a,∗
,YunLiu
a
, Zhen-jiang Zhang
a
, Jiang Zhu
b
, Ying Zhang
b
a
Key Laboratory of Communication and Information Systems (Beijing Jiaotong University), Beijing Municipal Commission of Education, Beijing, 100044, China
b
Carnegie Mellon University, Silicon Valley, Moffett Field, CA 94035, USA
article info abstract
Article history:
Received 16 November 2011
Received in revised form 27 April 2012
Accepted 9 May 2012
Available online 11 May 2012
Communicated by A.R. Bishop
Keywords:
Diffusion dynamics
Online social media
Individual behavior
Complex system
To characterize information propagation on online microblogs, we propose a diffusion model (SCIR)
which contains four possible states: Susceptible, contacted, infected and refractory. Agents that read the
information but have not decided to spread it, stay in the contacted state. They may become infected
or refractory, and both the infected and refractory state are stable. Results show during the evolution
process, more contacted agents appear in scale-free networks than in regular lattices. The degree based
density of infected agents increases with the degree monotonously, but larger average network degree
doesn’t always mean less relaxation time.
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
With the development of network technology, Internet has be-
come one of the most important media from which people gain in-
formation. Online social media have been widely used in daily life
as a way to express individual attitudes and emotions, and com-
municate with friends. Information about many significant events
in society often spreads on Internet first. As a result of conve-
nience and freedom, information on social media propagates more
quickly than in real society, and social media are now important
sources of online emergencies. As a typical representative, Twit-
ter, has become one of the most popular website applications in
microblogging services, fully demonstrating its strength as an ef-
fective medium. Twitter has 200 million registered users and over
190 million tweets posted every day [1].Alargenumberofpeo-
ple publish and share information on Twitter, and local discussions
launched by several users can cause public responses, and prop-
agate via a global scope. Research on Twitter can thus provide
valuable insight into understanding information diffusion on social
network sites [2,3].
Lots of research has been devoted to the propagation dynam-
ics, originating from an epidemic outbreak study. As the simplest
dynamical process, the susceptible-infected (SI) model [4,5] con-
*
Corresponding author at: Beijing Jiaotong University, School of Electronic and
Information Engineering, Room 607, South of No. 9 Teaching-Building, No. 3 Shang
Yuan Cun, 100044 Hai Dian District, Beijing, China. Tel.: +86 13811992620.
E-mail address: 08111029@bjtu.edu.cn (F. Xiong).
siders only two available states. A susceptible node can be in-
fected by an infected neighbor permanently with a spreading rate,
and thus all nodes become spreaders in the end. Unlike the SI
model, the susceptible-infected-susceptible (SIS) model [6–9] al-
lows nodes to recover and become susceptible again. It is thus
hard for the disease to infect all the population. The susceptible-
infected-refractory (SIR) model [10–14] introduces a refractory
state in which nodes cannot be infected. Infected nodes may en-
ter the refractory state spontaneously with a refractory rate. This
phenomenon accounts for the situation where patients may be im-
mune to a disease. In the dynamics, there is a threshold value of
spreading rate below which the disease cannot propagate in the
system. Meanwhile, rumor diffusion has a similar intrinsic mecha-
nism with epidemic dynamics. The above method of dynamics has
also been used in rumor propagation. In the rumor model [15–18],
the immune procedure takes place by agents’ interacting. When an
infected node meets another infected or refractory node, the orig-
inal node may become immune. Interaction between nodes may
help hamper the diffusion of rumor. The above models can be an-
alyzed using mean-field equations, and the final diffusion extent
can then be estimated from these equations. In these modes ex-
cept for the SI model, the infected state is temporary and unstable,
and it will change to other states.
With the further development of research on complex networks
[19–22], network topology has been taken into account for epi-
demic and rumor dynamics, as it may significantly change the
whole diffusion process [23–27]. In consideration of rumor prop-
agation in heterogeneous networks, degree based analytical evo-
lution equations were given. In their dynamics, rumor is easier
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http://dx.doi.org/10.1016/j.physleta.2012.05.021