BA模型的三种扩展

无标度网络的发现，使人类对于复杂网络的认识进入了一个新的天地．BA模型是对于这种新认识的第1个抽象模型．由于考虑了系统的成长性和连接的择优性，BA模型给人们带来了很多启发．但是BA模型的两个基本假定，对于解释许多现实中的现象来说过于简单，与现实的网络还有较大的距离．所以，作者试图对BA模型进行扩展，即根据现实中的网络，增添某些假定，并通过计算机模拟进行观察，以便进一步探索复杂网络系统的规律．对BA模型的扩充考虑了3个因素：择优选择的成本；边的重新连接；网络的初始状态．实验结果表明，在考虑了这些因素之后，BA模型的基本结论并没有变化，它们的影响在于演化过程的某些方面，例如在某些极端条件下的演变趋势等．

Three extensions for B-A model

The discovery of scale free network has opened new horizon for our understanding on complex system. The BA model is the first formal explanation for this understanding. Considering the growing and optimal connection, BA model provided a lot of enlightenment for us. However, the two basic assumptions in BA model are still too simple for explaining many real phenomena, there are quite far distance to real networks. In this paper, we try to expand BA model. Based on some real networks, we add some assumptions, and use computer simulation for observation. We have considered three factors: Cost of optimal selection, Re_connection of edges, initial state of the networks. Our results indicate that the basic feature and rules in scale free network are the same, but these factors still have some influence on the growing process, for instance, the evolvement in some extreme situation.