As networks grow in size and complexity, backbones become an essential network representation. Indeed, they provide a simplified yet informative overview of the underlying organization by retaining the most significant and structurally influential connections within a network. Network heterogeneity often results in complex and intricate structures, making it challenging to identify the backbone. In response, we introduce the Multilevel Backbone Extraction Framework, a novel approach that diverges from conventional backbone methodologies. This generic approach prioritizes the mesoscopic organization of networks. First, it splits the network into homogeneous-density components. Second, it extracts independent backbones for each component using any classical Backbone technique. Finally, the various backbones are combined. This strategy effectively addresses the heterogeneity observed in network groupings. Empirical investigations on real-world networks underscore the efficacy of the Multilevel Backbone approach in preserving essential network structures and properties. Experiments demonstrate its superiority over classical methods in handling network heterogeneity and enhancing network integrity. The framework is adaptable to various types of networks and backbone extraction techniques, making it a versatile tool for network analysis and backbone extraction across diverse network applications.

翻译：随着网络规模和复杂性的增长，骨干网络已成为一种重要的网络表示形式。事实上，通过保留网络中最重要且具有结构影响力的连接，骨干网络能够提供一种简化但信息丰富的底层组织结构概览。网络的异质性常常导致结构复杂且错综，使得骨干网络的识别颇具挑战。为此，我们提出了多层次骨干提取框架，这是一种有别于传统骨干方法的新颖方法。该通用方法优先考虑网络的介观组织。首先，它将网络分割为具有均匀密度的组件。其次，它使用任何经典的骨干提取技术为每个组件提取独立的骨干。最后，将各个骨干组合起来。该策略有效地解决了网络分组中观察到的异质性问题。对现实世界网络的实证研究突显了多层次骨干方法在保留网络基本结构和属性方面的有效性。实验表明，其在处理网络异质性和增强网络完整性方面优于传统方法。该框架可适应各种类型的网络和骨干提取技术，使其成为跨多种网络应用进行网络分析和骨干提取的多功能工具。