Efficiency-Controllable Random Walks on a Class of Recursive Scale-Free Trees with a Deep Trap
LI Ling1,2** , GUAN Ji-Hong1** , ZHOU Shui-Geng3,4
1 Department of Computer Science and Technology, Tongji University, Shanghai 2018042 Department of Basic Courses, Zhejiang Shuren University, Hangzhou 3100153 School of Computer Science, Fudan University, Shanghai 2004334 Shanghai Key Lab of Intelligent Information Processing, Fudan University, Shanghai 200433
Abstract ：Controls, especially efficiency controls on dynamical processes, have become major challenges in many complex systems. We study an important dynamical process, random walk, due to its wide range of applications for modeling the transporting or searching process. For lack of control methods for random walks in various structures, a control technique is presented for a class of weighted treelike scale-free networks with a deep trap at a hub node. The weighted networks are obtained from original models by introducing a weight parameter. We compute analytically the mean first passage time (MFPT) as an indicator for quantitatively measuring the efficiency of the random walk process. The results show that the MFPT increases exponentially with the network size, and the exponent varies with the weight parameter. The MFPT, therefore, can be controlled by the weight parameter to behave superlinearly, linearly, or sublinearly with the system size. This work provides further useful insights into controlling efficiency in scale-free complex networks.
出版日期: 2015-02-26
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2015, Vol. 32 
