Directed Q-Analysis and Directed Higher-Order Connectivity on Digraphs: A Quantitative Approach
摘要
Traditional graph analysis focuses on nodes and edges, that is, pairwise relationships. Yet many real-world networks, including biological, social, and communication networks, involve higher-order relationships in which multiple nodes interact simultaneously. This has led many to develop network topology analysis methods based on higher-order structures and higher-order connectivity, seeking to reveal complex interactions beyond node pairs. Many of the latter address only undirected networks. To overcome this, we lay out a mathematical formalism resting on directed clique complexes constructed from directed graphs (their "higher-order structures" or "simplicial structures''), stressing the interrelations between directed cliques (their "directed higher-order connectivities''), leading towards a more complete directed Q-analysis that allows quantifying, characterizing, and comparing similarities involving simplicial structures.
引用
@article{arxiv.2605.14178,
title = {Directed Q-Analysis and Directed Higher-Order Connectivity on Digraphs: A Quantitative Approach},
author = {Heitor Baldo and Luiz A. Baccalá and André Fujita and Koichi Sameshima},
journal= {arXiv preprint arXiv:2605.14178},
year = {2026}
}
备注
arXiv admin note: text overlap with arXiv:2409.09862