Structure Analysis Of Complex Networks Based On Entropy

In the past 100 years,development of science and technology have produced a lot of complex systems,such as world wide web,large scale online social network,power net in big city,traffic networks and so on.On the other hands,development of technology allowed us to describe those complex systems,such as ecological network,interaction between proteins,relation networks of proteins and genes.These complex systems have big scale and complex structure,it is very difficult to describe it use classic methods.On the other hand,we need to know more about these complex systems,because we need to maintain normal operation of these systems and sometime we need to control these complex systems.Therefore,requirement from real world has prompted birth of a new research filed:Complex networks.The research of complex networks has attracted many researchers from different research fields to focus on it,such as the researchers from computer science,physics,chemistry,biology and sociology.Complex networks have been wildly used in a lot of different research filed.And the research of complex networks proposed a lots of new methods in these research filed too.In the research of complex networks,one of the most important topic is research of complex networks' structure.In the research of complex networks' structure,there are four different important research fields:first,identifying influential nodes in it,second,measuring node's similarity in it,third,quantify structure complexity of it,fourth,quantify self-similarity in it.These four different research fields have have big influences on complex network.For example,identifying influential nodes in complex networks is basic of research on structure vulnerability and robustness.Measuring nodes' similarity is very important for research of link prediction and community structure detection in complex networks.If we want to know how complex of the complex networks,we need to quantify the structure complexity of it.And calculate the information dimension of complex network is a new way to check the self-similarity of complex networks.There are many classic methods have been proposed to solve these problems.In the thesis,the Shannon entropy and Tsallis entropy have been used on the research of complex networks' structure.The main work in this thesis can be divided into four parts:(1)A local structure entropy of each node to identify the influential nodes in complex networks is proposed.(2)A new method to measure the nodes' similarity based on relative entropy is proposed.(3)A new structure entropy of complex networks based on the Nonextensive entropy is proposed.(4)A new information dimension of complex networks which is based on the Nonextensive entropy is proposed.Entropy is one of the most important concept in statistical mechanics and information theory.In this thesis,we try to apply entropy into complex networks,to analysis the structure of it.