A Study On The Characteristics Of Two Kinds Of Regular Small World Networks

Complex networks have many potential applications in many fields such asnatural, social, biological, engineering technology. Many researchers are interestedin it. Randomness is in line with most network in the real world, while determinationof the networks is very hard to understand how do different nodes relate to each otherand how networks are shaped. So, the deterministic models for complex networksplay an indispensable role in the field of network model. Network model ofdeterministic way to structure consistent with the real system not only has importanttheoretical significance, but also has potential application value. The research of itstopological properties makes us to seize the local and global features of networks. Wepresent two new deterministic networks models, we study the relevant topologicalcharacteristics of two classes of small world phenomenon regular networks model byconstructing networks in this paper.We mainly introduce the background, the present situation and development ofthe complex network and the deterministic network model. Some main results arelisted in chapter1.Some of the concepts and definitions involved are list, some theories andformulas are presented in the calculation of the main results of this paper in chapter2.We mainly introduce the three regular network model, calculated its topologicalproperties and growth law. We give a calculation method of number of spanning treesin such three regular networks and derive the formulas and the entropy of number ofspanning trees in chapter3.We mainly investigate the four regular network model and analysis its basictopological properties. Then we give a calculation method of number of spanningtrees in such four regular networks and derive the formulas and the entropy of numberof spanning trees in chapter4.We summarizes the research conclusion in this paper, and listed some issues canbe further discussed in chapter5.