One of the important Natural Language Processing applications is Text Summarization, which helps users to manage
the vast amount of information available, by condensing documents' content and extracting the most relevant facts or topics included. Text Summarization can be classified according to the type of summary: extractive, and abstractive. Extractive summary is the procedure of identifying important sections of the text and producing them verbatim while abstractive summary aims to produce important material in a new generalized form. One of recent approaches to achieve the abstractive summary is converting the original text to a graph, reducing this graph, and then converting the reduced graph into summarized text. In this paper, several approaches for graph reduction are presented. These approaches have different applications in different fields. Using a working example, the paper describes in progress research to apply graph reduction techniques in abstractive text summarization.