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Chao Gao ( [e-mail]) is a professor in the College of Computer and Information Science, Southwest University, Chongqing, China, and a visiting scholar in the Humboldt University of Berlin, Germany.

Zhen Su ( [e-mail]) is pursuing a master’s degree in the College of Computer and Information Science, Southwest University, Chongqing, China.

Jiming Liu ( [e-mail]) (corresponding author) is a professor of computer science and associate vice president (research) at Hong Kong Baptist University, Hong Kong, China.

Jürgen Kurths (Juergen. [e-mail]) is a professor of nonlinear dynamics in the Humboldt University of Berlin, Germany, and Chair of the Research Domain Transdisciplinary Concepts in the Potsdam Institute for Climate Impact Research, Potsdam, Germany.

© 2019 ACM 0001-0782/19/2 $15.00

source nodes are distributed over only one community, thereby suppressing global diffusion.

However, diffusion is quite different when nodes characterized by relatively least centrality are viewed as sources. Source nodes under such conditions are distributed over more communities and more likely to facilitate global diffusion. Moreover, the worst case is unlikely to appear due to the relatively greater proportion of low-degree nodes in a network. That is why there are fewer red nodes in “C0,” “C1,” “C2,” “C3,” and “C4” than blue nodes. As the two propagation processes in Figure 6—maximum-degree-based and minimum-degree-based—proceed, such phenomenon will intensify. Finally, the various diffusion scenarios we have addressed also increase the fluctuation of crossover points.

For networks with weak community structures, the increasing proportion of intracommunity links makes global diffusion more likely, making crossover points relatively stable.

Conclusion

We have explored the nonlinear crossover of two diffusion processes— cen-tral-user-based and boundary-user-based—triggered by two opposite initial states in networks with community structure. We first considered the universality of the crossover phenomenon, then offered a detailed comparison with respect to the influence of community structure and initial proportion of source nodes on the diffusion process. The results were twofold: Networks with weak community structure could increase the stability of crossover points; and compared to the influence of community structure, the increment of the initial source nodes is the primary factor leading to an earlier crossover phenomenon.

The crossover phenomenon shows
the topology of a network is a major
factor affecting the diffusion process.
A deep understanding of diffusion
dynamics requires consideration of
both network topology and dynamical
correlations. Many popular theoreti-
cal approaches (such as mean field,
dynamical message passing, and pair-
wise approximation) are used to study
the dynamics of different kinds of in-
formation diffusion, but the difficulty
of capturing both network topology
and dynamical correlations remains
an open topic. 20 Even with the con-
tinuous-time Markov approach, the
complicated master equations lead
to yet another challenge—that the
approach is unlikely to directly yield
analytical or numerical results for
large-scale networks. Studies inves-
tigating the balance between poten-
tial diffusion dynamics and solving
computational complexity are still
being challenged.

This article has offered insight into the dynamics of information diffusion in community-based networks. For instance, compared with the ability of nodes with relatively greater centrality to dramatically enhance diffusion speed at the initial stage, nodes with relatively least centrality could in fact have a greater propagation effect in the long term, especially when a network includes more initial source nodes. However, we are not saying nodes with relatively least centrality are critically important. It is the topological structure that establishes an explicit and complex connection between the two kinds of nodes. In some cases, such connections suggest users with relatively least centrality should be taken into consideration, as they could still significantly influence global diffusion.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (grant No. 61402379), Hong Kong Research Grants Council (No. HKBU12202415), CQ CSTC (grant No. cstc2018jcyjAX0274), the Fundamental Research Funds for the Central Universities (grant No. XDJK2016A008), and Chongqing Graduate Student Research Innovation Project (grant No. CYS17075).

 

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