Complex Network Modeling And Research On Coarse Graining Method

With the rapid development of information and computer technology,many complex systems in real world(such as the power networks,the Internet,and the communications-transportation networks,etc.)have become increasingly large and complex,and these real-world systems can be abstractly represented by complex network,then be analyzed and studied.Therefore,complex networks have gradually become the research hotspots in various disciplines in recent years.In particular,in the exploration of the structure and function of large-scale networks and network modeling are the important subject in the network sciences.At the end of the last century,the introduction of the WS small-world and BA scale-free model not only greatly promoted the development of complex networks,but also enabled people to understand in essence the small-world and scale-free nature of many real-world networks.However,with the advancement of science and technology and the development of complex networks,many unrelated things in the traditional sense are connected with each other,and the connections are becoming more and more intimate,forming the networks with complex and diverse structures.It forces people to constantly propose new network models to simulate and explain the structure and functions of various real-world networks.At the same time,the size of many real-world networks is very huge.Computation and simulation experiments will take huge time and material in the study of these large-scale networks,making many existing methods of studying the medium and small-scale networks difficult to implement.A promising way is to coarse grain,aiming at reducing the original networks into the small and medium-sized ones by merging the nodes that share the similar characteristics,while preserving certain properties of the original networks.Coarse graining technology is one of the important methods to study large-scale complex networks currently.The paper focus on network modeling and the study of coarse graining method,the main points are summarized as follows:(1)A novel neighbor-preferential growth(NPG)network model is proposed.The new model can reproduce small-world and scale-free features,and its synchronizability is much stronger than that of BA networks,even stronger than that of synchronization-optimal growth networks.Meanwhile,the NPG model is robust with respect to random attacks and is fragile to specific removal of a small fraction of nodes.(2)The star-like scale-free(SLSF)network model with tunable clustering is put forward.It has the characteristics of free-scale,small-world and star-like.Interestingly,not only the power exponent is related to the fixed nodes number ? and the edge-adding number m,but also the clustering coefficient can be tuned by 8 and m in the proposed model.The difference is that 8 has a great influence on the clustering coefficient,and m has small effect on it,which makes it can be tuned in a big interval.Further studies,show that the synchronizability of SLSF networks will be stronger with the number of fixed nodes increasing.(3)A new coarse graining technique,which called generalized degree coarse graining(GDCG),is introduced.The nodes are clustered according to the distribution of generalized degrees during the coarse-graining processes,and the generalized degree of the nodes can be adjusted by the parameter p in order to better maintain some significant properties of the original networks.Compared with the existing coarse-graining methods,the GDCG method is only based on the generalized degree,which is not only simple and operable,but also keeps some statistical properties and the synchronizability of the initial networks.Moreover,the size of the coarse-grained networks can be chosen freely in the proposed method.The related investigations have provide a new insight for the study of large-scale complex networks.