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Title: A general stochastic model for studying time evolution of transition networks
Authors: Zhan, C
Tse, CK 
Small, M
Keywords: Dynamic complex network
Simulation algorithm
Stochastic process model
Issue Date: 2016
Publisher: North-Holland
Source: Physica A. Statistical mechanics and its applications, 2016, v. 464, p. 198-210 How to cite?
Journal: Physica A. Statistical mechanics and its applications 
Abstract: We consider a class of complex networks whose nodes assume one of several possible states at any time and may change their states from time to time. Such networks represent practical networks of rumor spreading, disease spreading, language evolution, and so on. Here, we derive a model describing the dynamics of this kind of network and a simulation algorithm for studying the network evolutionary behavior. This model, derived at a microscopic level, can reveal the transition dynamics of every node. A numerical simulation is taken as an “experiment” or “realization” of the model. We use this model to study the disease propagation dynamics in four different prototypical networks, namely, the regular nearest-neighbor (RN) network, the classical Erdös–Renyí (ER) random graph, the Watts–Strogátz small-world (SW) network, and the Barabási–Albert (BA) scalefree network. We find that the disease propagation dynamics in these four networks generally have different properties but they do share some common features. Furthermore, we utilize the transition network model to predict user growth in the Facebook network. Simulation shows that our model agrees with the historical data. The study can provide a useful tool for a more thorough understanding of the dynamics networks.
ISSN: 0378-4371
EISSN: 1873-2119
DOI: 10.1016/j.physa.2016.07.034
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