ArticleScientific reports2021
Graph hierarchy: a novel framework to analyse hierarchical structures in complex networks.
Article in Scientific reports, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 8 papers.
What it found
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
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Who cites it
8 citing papers in PubMed, 23 citations in OpenAlex.
- IgM and IgG Epitope Mapping of the Porin Outer Membrane Protein-2a fromInternational journal of molecular sciences · 2026Article
- Harnessing the analog computing power of regulatory networks with the Regulatory Network Machine.iScience · 2025Article
- Dynamics of IgM and IgA Antibody Response Profile AgainstInternational journal of molecular sciences · 2025Article
- LSD flattens the hierarchy of directed information flow in fast whole-brain dynamics.Imaging neuroscience (Cambridge, Mass.) · 2025Article
- New Epitopes for the Serodiagnosis of Human Borreliosis.Microorganisms · 2024Article
- Mapping IgA Epitope and Cross-Reactivity between Severe Acute Respiratory Syndrome-Associated Coronavirus 2 and DENV.Vaccines · 2023Article
- Hierarchy Depth in Directed Networks.Entropy (Basel, Switzerland) · 2022Article
- Directed network Laplacians and random graph models.Royal Society open science · 2021Article
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
4 authors at 4 institutions in 1 country.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Trophic coherence, a measure of a graph's hierarchical organisation, has been shown to be linked to a graph's structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their functional properties, partition and rank the vertices accordingly. Trophic levels and hence trophic coherence can only be defined on graphs with basal vertices, i.e. vertices with zero in-degree. Consequently, trophic analysis of graphs had been restricted until now. In this paper we introduce a hierarchical framework which can be defined on any simple graph. Within this general framework, we develop several metrics: hierarchical levels, a generalisation of the notion of trophic levels, influence centrality, a measure of a vertex's ability to influence dynamics, and democracy coefficient, a measure of overall feedback in the system. We discuss how our generalisation relates to previous attempts and what new insights are illuminated on the topological and dynamical aspects of graphs. Finally, we show how the hierarchical structure of a network relates to the incidence rate in a SIS epidemic model and the economic insights we can gain through it.
Identifiers
What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.