Development and Application of Complex Networks

AI+Wen-wen　LIU+Hao

【Abstract】The rise time of the complex network research is not long， but the research on complex network is in the ascendant. Meanwhile， complex network theory has been widely used in many aspects， and it has potential application value. In this paper， we concentrate on the complexity and topological characters， and the application of the complex networks.

【Key words】Complexity； Topological characters； Complex networks

1 Introduction

Many systems in the real world can be described by complex networks， such as， in social network： research cooperation network， company director network； in information network： the world-wide web， scientific research citation network， language network； in technical network： internet， power network， aviation network； metabolic networks and protein networks in biological networks. The complexity of the real network system is mainly reflected in the three aspect： first of all， the structure of the network is very complex， the connection between the network nodes， so far is still not a very clear concept； secondly， the network is evolving， the network node is constantly increasing， The connection between the nodes is constantly growing， and there are a variety of connections between them； third， The dynamics of the network is complex， and each node itself can be a nonlinear system[1].

Due to the large scale of the real-world network， the interaction between nodes is complex， and the topology structure is largely unknown or not. For more than two hundred years， people have experienced three stages to describe the topological structure of the real system. From late 1950s to the end of 90s， the random network of large-scale network without a clear design principles mainly with simple and easy to be accepted by most people to describe the idea of random graphs， dominate the research of complex network for forty years； until recent years， scientists have found a large number of real networks are neither regular networks nor random networks， but has statistical characteristics are different with the former two networks， is one of the most influential small world networks and scale-free networks. The discovery of these two kinds of networks， set off a boom in the study of complex networks.

2 Application of the networks

Complex networks just put forward， showing a broad application prospects， and its application in engineering technology， social， political， medical， economic， management and other aspects[2].

2.1 The social field

Infectious disease a great threat to mankind： aids people： 2003 SARS shiver all over though not cold on the macro economy and the safety of human life have a huge negative impact； at present， avian influenza has also become a focus of the world attention. So， in a particular social network， infectious disease caused by contact between the dissemination of popular？ Decision makers how to control these diseases， will minimize the losses？ These problems may find the answer from the complex network there. In recent years， scientists have considered the main characteristics of different systems， and put forward a number of targeted immune methods for disease prediction， prevention and immunization provides a scientific program.

2.2 The political phase

In addition to the social sphere， complex networks have also begun to show practical value in politics. Nowadays， terrorism has been listed as one of the ten major hazards in twenty-first Century， in the United States in 911 event let the nation still scared. For the organization of terrorism， crime these requires the destruction of network， people can use the complex network theory， the capture of the arrest of its main characters， can destroy the network， make its function disorder， in order to safeguard the human social and political stability. Network theory can also be used to reveal the organization of government members， hierarchical relationships， and even successful simulation of political elections， analysis of the impact of some factors on the outcome of the election.

2.3 The medicine filed

In the field of medicine， complex network also has its important application value. Many infectious diseases are expensive， and the number is limited， it is impossible for everyone to be vaccinated. This approach is likely to be the most useful for countries and regions that are unable to take care of the whole country， while allocating the cost of AIDS， smallpox， and so on. In the pharmaceutical industry， dependent on a hub node， provides a new method for drug research： it is possible to find such drugs can hubs targeted attack cells or bacteria， to kill them and will not affect the healthy tissue[3].

In addition to the above applications， the study of complex networks， for many other areas is also valuable. For example， the small world thought for BP network， BP network can reduce the learning time and error， can be better applied to many fields of data mining， speech recognition， image processing and pattern recognition BP network makes； in addition， the complex network for Hopfield network， can change the function of associative memory neural network.

3 The Signification of complex networks

Although every subject in the structure of the research object， all concrete results are very rich， but from the system level， across the material system， the specific research results of biological system and social economic system， that is system level is not much， the connotation of system level has yet to complete this the complex network is integrated. Self-organization theory in the past， nonlinear theory and complexity theory research and the formation of the new theory. The rise of complex network， to expand the field of vision for the study of system science， and provides a new perspective.

4 Conclusion

Complex network as a general abstract and description of complex systems， as the structure of complex systems， it highlights the structure of the system. It can be said that any complex system can be used as a complex network to study. Using complex networks of complex systems， can help people to understand the structure of the system， with the in-depth study of complex networks and network system evolution theory research in-depth work， research on the complex system evolution will appear new breakthrough results； in turn， results of the complex networks has certain inspiration and reference to explore the complexity of F training； can of course to study the network from the perspective of science， which is the new perspective of network research. It can be seen that using the network theory to study the system is a new research method of system science.

【References】

[1]Newman M E J. Models of the small world[J]. Journal of Statistical Physics， 2000， 101：819-841.

[2]Strogatz S H. Exploring complex networks[J]. Nature， 2001， 410：268-276.

[3]Albert R， Barabfasi A-L. Statistical mechanics of complex networks[J]. Reviews of Modern Physics，2002，74（1）：47-97.

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