Dissertation > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Graph Theory

Research into the Complexity and Community Structure of the Engineering Software Network

Author ZhangZhiHua
Tutor FengZuo
Course Applied Computer Technology
Keywords engineering information software formats conversion complex networks small-world networks community structure Coulomb’s Law
CLC O157.5
Type Master's thesis
Year 2011
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Based on the engineering information, aiming at the problem that there exists incompatibility between the information and its using systems during the long-term secure saving and reliable calling of the engineering information, the conversion between the engineering software formats is studied in order to apply to different systems. Meanwhile, two kinds of networks of the software formats conversion are established. On the basis of these networks, the complex network theories are led into the field of engineering information. Furthmore, the topology of these networks is studied in-depth, the models of these networks are verified, and the community structures of the networks are analyzed.In the dissertation, more comprehensive attribute information of the engineering software is collected. After that we establish a network with a moderate scale, and during this process, we take the software fomats as its nodes and the conversion of the formats as its arcs. On the basis of the network, we select reasonable weighting strategy to weight the software formats network and establish a new weighted network.Adopting the analysis method of the complex network, we analyze the unweighted network from the static characteristic indices of the complex network such as the average path length, clustering coefficient and node-degree distribution of the network; and we also analyze the weighted network from the weighted average path length, the weighted clustering coefficient, edge weight distribution, node strength distribution, nodes weight difference and weighted correlation. The results indicate that the unweighted software formats network is a small-world network and the weighted one is a small world network with positive correlation.From a series classical algorithms of the community structure detecting, we select some ones to detect the community structure of the software formats network such as the spectral method based on the Normal matrix, original GN algorithm, Newman algorithm using the heap structure and Blondel method. From the results of the experiments we generalize the reasonable way to understand the community structure. Furthermore, through the community structure, we find the close-sparse relations of the different formats nodes, and this can provide the foundation for the formats conversion selection.In the dissertation, the Coulomb’s Law in the physics is introduced to the community structure detecting in the complex network. According to the Coulomb’s Law, we propose a mathematical model of the community force, and take it as an evidence of the community structure detecting. Then the algorithm based on the Coulomb’s Law is proposed. In comparision with the original GN algorithm, the results indicate the new algorithm achieve good results.

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