TY - CHAP

T1 - A general model for studying time evolution of transition networks

AU - Zhan, C.

AU - Tse, C.K.

AU - Small, Michael

PY - 2016

Y1 - 2016

N2 - © 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.

AB - © 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.

U2 - 10.1007/978-3-662-47824-0_14

DO - 10.1007/978-3-662-47824-0_14

M3 - Chapter

SN - 9783662478233

VL - 73

T3 - Understanding Complex Systems

SP - 373

EP - 393

BT - Complex Systems and Networks

A2 - null, Jinhu Lu, Zinghou Yu, Guanrong Chen, Wenwu Yu

PB - Springer

ER -