Complex Network Theory-based Input-output Correlation Analysis

The national economy is a complex system composed of many production departments and consumption departments which have different characters but interact with each others. The production of each department depends on the products of the other production departments as its inputs; meanwhile the total products of this department decompose into final consume demands and inputs needed by the other production departments. In order to study the universal interdependence of the departments and to analyze the national economic structure, the modeling and analysis of the input-output relevancy of national economic departments based on complex network theory are proposed in this paper for the first time.In this paper, the input-output relevancy is studied by complex network theory combining the statistical with comparative analysis methods, and quantitative with qualitative analysis methods. The research work was carried out following the route from the input-output relevancy network modeling to structure characters analysis, then empirical analysis with the national economic data of our country.The paper first gives the research background of the input-output relevancy, recalls the research history, reviews the basic concepts and models, and then presents the idea for input-output relevancy research by complex network theory. At the same time, the paper also reviews the research history and current status, the basic concepts and models. which is the groundwork for the further study of complex network. In particularly, the rigorous statistical test process for power law distribution is given to ensure the preciseness of the conclusion about distribution.As a common method to analyze the relations among the agents in a complex system, the DEMATEL method is improved based on complex networks. An improved DEMATEL method is proposed in this paper. The input-output relevancy of the national economic departments is discussed from the four aspects including influence degree, influenced degree, central degree and the reason degree to show the status and effects of each industry department by analyzing the national economic input-output data.The input-output relevancy network model for the national economic system is established based on the complex network theory. This network is not only a weighted network. but also a directed multiple network with self-loop. The main statistical network characters of the input-output relevancy network including degree and degree distribution, weight and weight distribution. clustering coefficient, the shortest path length, etc, are discussed by deeply analyzing the data from the Input-output Table of our country. The results show that: the network is close in topology that a few departments have input or consume relations with almost all departments; the weight distribution follows a power law; the determinant for the department importance is its out-strength; the weighted clustering coefficient is small that big weights take place among a few departments while the input or consume is small among most departments; etc.The measures of clustering and correlation are given and compared from the viewpoints of topology and weighted network respectively. The national economic structure of our country is set as an example to reveal the structure characters of the input-output relevancy network and the economic meanings implied in it by analyzing the network clustering and correlation.Finally, the community structure concept in complex network is introduced into the input-output relevancy network to investigate and analyze the national economic industry structure. According to the specialty of the input-output relevancy network, the community detecting algorithm is proposed combing spectral analysis, fuzzy K-meanmethod and modularity (Q function) optimization. The national economic of our countryis partitioned into four communities by using this algorithm, and then the components of the four communities are discovered, moreover, the existing status of the public departments in different communities is discussed.This work analyzes the input-output relevancy and industry structure of our country based on complex network theory and method under the guidance of complexity science, which is a practical application in the national economic system.