  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.
