A general model for studying time evolution of transition networks

C. Zhan, C.K. Tse, Michael Small

    Research output: Chapter in Book/Conference paperChapter

    2 Citations (Scopus)

    Abstract

    © Springer-Verlag Berlin Heidelberg 2016. 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, referred to as transition networks in this chapter, represent practical networks of rumor spreading, disease spreading, language evolution, and so on. Here, we derive a general analytical model describing the dynamics of a transition network and derive a simulation algorithm for studying the network evolutionary behavior. By using this model, we can analytically compute the probability that (1) the next transition will happen at a given time; (2) a particular transition will occur; (3) a particular transition will occur with a specific link. 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, theWatts-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 of transition networks.
    Original languageEnglish
    Title of host publicationComplex Systems and Networks
    Subtitle of host publicationDynamics, Controls and Applications
    EditorsJinhu Lu, Zinghou Yu, Guanrong Chen, Wenwu Yu
    PublisherSpringer
    Pages373-393
    Number of pages21
    Volume73
    ISBN (Print)9783662478233
    DOIs
    Publication statusPublished - 2016

    Publication series

    NameUnderstanding Complex Systems

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