Hierarchical Cutting of Complex Networks Performed by Random Walks

Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the situation in which the connections traversed by each step of a...

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Bibliographic Details
Main Authors Benatti, Alexandre, Costa, Luciano da F
Format Journal Article
LanguageEnglish
Published 11.03.2024
Subjects
Computer Science - Social and Information Networks
Physics - Physics and Society
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Summary:Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the situation in which the connections traversed by each step of a uniformly random walks are progressively removed, yielding a successively less interconnected structure that may break into two components, therefore establishing a respective hierarchy. The sizes of each of these pairs of sliced networks, as well as the permanence of each connected component, are studied in the present work. Several interesting results are reported, including the tendency of geometrical networks sometimes to be broken into two components with comparable large sizes.
DOI:10.48550/arxiv.2403.06876