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With the development of science and technology, more and more practical problems in life need to use mathematical models to analyze and to solve. So the utility ration of digital technology is becoming higher and higher in terms of discrete structural problems, which has powerfully promoted the development of network diagram theory, solving a lot of difficulties in people's production and living, improving work efficiency and promoting further development of science and technology. This paper mainly provides an analytic study in the respect of computerized algorithms and displaying methods of network diagrams. Introduction The 21st century is a period of rapid development of network information technology, during which computer technology has become matured and humans have made much progress in the development of science and technology. Beneficial from the progressive development, the tight coupling of network diagram theory and computer technology are provided with advantageous conditions. Especially in the respect of graph entity and graphic relation, by the application of network diagram theory network diagrams can be better optimized in the quantitative and qualitative treatments. In recent years, driven by information technology and digital technology, network diagram theory has developed rapidly, of which the display and control algorithm have reached the most rapid development as well as become a hot spot of research in recent years. Summary of the Development of Network Diagram Theories In real life many practical problems in China can be solved by means of establishing mathematical models. The research involved in this respect can be traced back to as early as 1850 AD. For example, in Europe the research involved the question of the "queen” in chess as how to both use the least to obtain the least squares, which is exactly the prototype of the earliest network diagram. It was not until the 18th century that people developed diagram theory in terms of the study of points and lines to such an extent that they formed a graphic science based on the combination of points and lines. In 1736, Euler posed the question as “whether or not it is possible to cross each of the seven bridges exactly once in the case of no repeated approach adopted”, assuming the question unanswerable and gave it a rigorous justification—a move that indicates the realization of digital transformation of abstract problems. Since then graph theory has been turned into a theory applied to many areas. Until the 1960s, Berge for the first time introduced several concepts of computerized algorithms in graph theory. After that, Ore introduced control algorithm in graph theory for the first time. Thus the real form the network diagram theory came into being International Conference on Computational Science and Engineering (ICCSE 2015) © 2015. The authors Published by Atlantis Press 333 and has promoted the development of the combination of mathematics and computer network technology. Fig. 1 is the automatically generated process of a network diagram. Figure 1 Automatically Generated Process of a Network Diagram Analyses of the Computerized Algorithms and Displaying Methods of Network Diagrams An Analysis with Dot Notation Control Algorithm. Dot notation control algorithm is defined by J.E. Dunbar for the first time in 1995, which mainly studies local dominant problems, a variety for the study of local dominant theory. In 2011, on the basis of dot notation control algorithm Michael A. Henning furthers the research and puts forward signed total control algorithm. There are essential differences between the two algorithms. Dot notation control algorithm requires conditions to be met on closed neighborhood of the dot while signed total control algorithm requires conditions to be met on open neighborhood of the dot. As regards China’s research on graphic theory, Xing Huaming introduces the issues of the minimum and the maximum and analyzes the lower boundary range of signed total control algorithm in 2003. On this basis, Michael A. Henning provides further analysis and research and sums up specific network diagrams. Wang Junxiu makes comprehensive improvement in terms of the problems of the lower boundary and proposes a more perfect boundary ratio in 2006. In 2009, Lv Xinzhong et al. further the study of signed total control algorithm and enrich its content. Leaning on the basis of predecessors’ studies, Xu Baogen also for the first time changes of signed total control algorithm into antisigned total control algorithm, thus promoting the further development of the research. Edge Symbol Control Algorithm. Early this century, Xu Baogen proposes edge symbol control algorithm for the first time, which define the boundary control algorithm. Then he continues the research on edge symbol control algorithm and elicits the upper and lower boundaries of general network diagrams and the exact value of some special symbols of network diagrams. Reducing edge control algorithm is transformed from signed edge domination algorithm. They are different in range of function value as the former changes the latter’s range of function value {-1,1} into {-1,0,1}. In actual research, reducing edge control algorithm is more difficult than other control algorithms, leading to less research findings. 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An Inquiry for Computerized Algorithms and Displaying Methods of Network Diagrams