A definition of network entropy is presented, and as an example, the relationship between the value of network entropy of ER network model and the connect probability p as well as the total nodes N is discussed. The theoretical result and the simulation result based on the network entropy of the ER network are in agreement well with each other. The result indicated that different from the other network entropy reported before, the network entropy defined here has an obvious difference from different type of random networks or networks having different total nodes. Thus, this network entropy may portray the characters of complex networks better. It is also pointed out that, with the aid of network entropy defined, the concept of equilibrium networks and the concept of non-equilibrium networks may be introduced, and a quantitative measurement to describe the deviation to equilibrium state of a complex network is carried out.
A definition of network entropy is presented, and as an example, the relationship between the value of network entropy of ER network model and the connect probability p as well as the total nodes N is discussed. The theoretical result and the simulation result based on the network entropy of the ER network are in agreement well with each other. The result indicated that different from the other network entropy reported before, the network entropy defined here has an obvious difference from different type of random networks or networks having different total nodes. Thus, this network entropy may portray the characters of complex networks better. It is also pointed out that, with the aid of network entropy defined, the concept of equilibrium networks and the concept of non-equilibrium networks may be introduced, and a quantitative measurement to describe the deviation to equilibrium state of a complex network is carried out.
LI Ji;WANG Bing-Hong;WANG Wen-Xu;ZHOU Tao. Network Entropy Based on Topology Configuration and Its Computation to Random Networks[J]. 中国物理快报, 2008, 25(11): 4177-4180.
LI Ji, WANG Bing-Hong, WANG Wen-Xu, ZHOU Tao. Network Entropy Based on Topology Configuration and Its Computation to Random Networks. Chin. Phys. Lett., 2008, 25(11): 4177-4180.
[1] Erd\"{os P and Renyi A 1960 Publications of the Mathematica Institute of the Hungarian Academy of Sciences 5 17 [2] Faloutsos M et al 1999 Comput. Commun. Rev. 29 251 [3] Pastor-Satorras R et al 2001 Phys. Rev. Lett. 87 258701 [4] Newman M E J 2001 PNAS 98 404 [5] Li M et al 2007 Physica A 375 355 [6] Watts D J and Strogatz S H 1998 Nature 393 440 [7] Barab\'{asi A L et al 2000 Science 287 2115a [8] Albert R and Barab\'{asi A L 2002 Rev. Mod. Phys. 74 47 [9] Newman M E J 2003 SIAM Rev. 45 167 [10] Wang X F 2002 Int. J. Bifur. Chaos 12 885 [11] Holme P and Kim B J 2002 Phys. Rev. E 65 026107 [12] Klemm K and Egu\'{\iluz V E 2002 Phys. Rev. E 65 036123 [13] Andrade Jr J S et al 2005 Phys. Rev. Lett. 94 018702 [14] Wang W X et al 2005 Phys. Rev. Lett. 94 188702 [15] Zhou T et al 2005 Phys. Rev. E 71 046141 [16] He Y et al 2004 Acta Phys. Sin. 53 1710 (in Chinese) [17]Li J et al 2006 Acta Phys. Sin. 55 4051 (in Chinese) [18] Shannon C E A 1948 Bell System Techn. J. 27 379 Shannon C E A 1948 Bell System Techn. J. 27 623 [19] Sole R V and Valverde S 2004 Information Theory of Complex Networks: on Evolution and Architectural Constraints, Lect. Notes Phys. 650 189 (Berlin: Springer) [20] Allegrini P et al 2004 Chaos Solitons Fractals 20 95 [21]Wang W N et al 2004 Chin. Phys. Lett. 21 243 [22] Tan Y J and Wu J 2004 The Systems Engineering Theory Practices (6) (in Chinese) [23] Wilk G et al 2004 Acta Phys. Polonica B 35 871 [24] Marr C and Hutt M T 2005 Physica A 354 641 [25] Venkatasubramanian V et al 2006 Aiche J. 52 1004 [26] Fu B B and Gao Z Y 2006 Chin. Phys. Lett. 23 520 [27] Wang B et al 2006 Physica A 363 591 [28] Lezon T R et al 2006 Proc. Nat. Acad. Sci. U.S.A. 103 19033 [29] Xie Y B, Zhou T and Wang B H 2008 Physica A 387 1683
2008, Vol. 25 
