## 1 Introduction  
Automatic text summarization is a crucial task in the field of natural language processing (NLP) that aims to reduce a text document to its most essential content, thereby making the breadth of information more manageable and accessible [1]. With the exponential increase in digital content, the need for effective summarization systems that can generate concise and coherent summaries has become more pronounced [2]. Extractive summarization, one of the two primary types of summarization techniques, involves selecting significant sentences or fragments from a text and compiling them to form a summary. Unlike abstractive summarization, which involves rewriting to capture the essence of the information, extractive methods ensure that the veracity of the original text is maintained [3]. The traditional approaches to extractive summarization have largely been centered around statistical and linguistic features such as the frequency and positional value of words, sentence length, and document structure. However, these methods often fail to capture the deeper semantic relationships within the text and the contextual nuances that are critical to producing summaries that are not only concise but also rich in content and coherent in narrative structure [4]. Recent advances in deep learning have led to the development of models that can better understand and process the complexities inherent in natural language [5; 6; 7]. Techniques such as sequence-to-sequence models, attention mechanisms, and neural embeddings have substantially improved the performance of summarization systems [8; 9]. Despite these advancements, the challenge of integrating and leveraging diverse contextual relationships within a document remains a significant hurdle [10; 11]. To address these challenges, the concept of using hypergraphs in text summarization has been proposed [12]. Hypergraphs allow for a more flexible representation of relationships within data, extending beyond the pairwise links captured by traditional graph models [13]. In document summarization, hypergraphs can represent complex interactions among multiple sentences or segments, facilitating a richer and more integrated understanding of the text's structure and thematic elements [14; 15; 16; 17]. However, while hypergraphs provide a powerful framework for data representation, their potential in extractive summarization has not been fully exploited, particularly in terms of effectively homogenizing and contextualizing the information across various document elements. This gap points to the need for a sophisticated approach that not only constructs a comprehensive hypergraph of the document but also processes it through advanced machine learning techniques to extract the most relevant content. This work introduces Multi-element Contextual Hypergraph Extractive Summarizer (MCHES), a novel framework designed to revolutionize extractive summarization. MCHES innovatively combines the representational benefits of hypergraphs with the latest advancements in contextual embeddings and attention mechanisms. Our main contributions are as follows:  
* We propose a unique method for constructing a multi-element hypergraph that captures extensive semantic, narrative, and discourse relationships within texts, offering a more nuanced understanding of document structure. * We develop the Contextual Homogenization Module (CHM), which effectively integrates the heterogeneous information present in different types of hyperedges, creating a uniform feature space that enhances data processing. * Our Hypergraph Contextual Attention Module (HCA) implements a dual-level attention mechanism, refining the focus on the most informative parts of the hypergraph and significantly improving the relevance and coherence of the generated summaries. * The Extractive Read-out Strategy we introduce optimizes the selection of sentences for the summary based on a combination of their intrinsic content value and their contextual importance, as mediated by their hypergraph connections.