In this paper, the concept of natural homomorphism for graph is presented. Furthermore, the method of reducing information graph and keeping the capability of processing information is given.

本文引入图的自然同态概念，并据此给出对信息图进行归约和保持信息处理能力的方法。

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Studying the condition about the natural partial order on it. And characterized the homomorphism between regular semigroups, discussing the conditions about the special homomorphism image.

给出了有关自然偏序的的两个重要条件刻划，对具有逆断面的正则半群之间的同态进行了刻划，讨论了具有逆断面的正则半群的特殊同态像的条件。

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