ArticleRoyal Society open science2020
How directed is a directed network?
Article in Royal Society open science, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 16 papers.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
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.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
16 citing papers in PubMed, 62 citations in OpenAlex.
- Optimal dismantling of directed networks.Nature communications · 2026Article
- Article
- Disrupted Brain Hierarchical Organization in Alzheimer's Disease Progression.medRxiv : the preprint server for health sciences · 2025Article
- Urbanisation Drives the Decoupling, Simplification, and Homogenization of Aquatic and Terrestrial Food Webs.Ecology letters · 2025Article
- LSD flattens the hierarchy of directed information flow in fast whole-brain dynamics.Imaging neuroscience (Cambridge, Mass.) · 2025Article
- Causal Hierarchy in the Financial Market Network-Uncovered by the Helmholtz-Hodge-Kodaira Decomposition.Entropy (Basel, Switzerland) · 2024Article
- How biotic interactions structure species' responses to perturbations.Proceedings. Biological sciences · 2024Article
- Treatment effects in epilepsy: a mathematical framework for understanding response over time.Frontiers in network physiology · 2024Article
- Article
- Influence and influenceability: global directionality in directed complex networks.Royal Society open science · 2023Article
- Strong connectivity in real directed networks.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
- Disruption of international trade and its propagation through firm-level domestic supply chains: A case of Japan.PloS one · 2023Article
- Hierarchy Depth in Directed Networks.Entropy (Basel, Switzerland) · 2022Article
- Directed network Laplacians and random graph models.Royal Society open science · 2021Article
- Graph hierarchy: a novel framework to analyse hierarchical structures in complex networks.Scientific reports · 2021Article
- Money flow network among firms' accounts in a regional bank of Japan.EPJ data 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
3 authors at 2 institutions in 1 country.
Funding
No grant is acknowledged in the PubMed record.
Abstract
The trophic levels of nodes in directed networks can reveal their functional properties. Moreover, the trophic coherence of a network, defined in terms of trophic levels, is related to properties such as cycle structure, stability and percolation. The standard definition of trophic levels, however, borrowed from ecology, suffers from drawbacks such as requiring basal nodes, which limit its applicability. Here we propose simple improved definitions of trophic levels and coherence that can be computed on any directed network. We demonstrate how the method can identify node function in examples including ecosystems, supply chain networks, gene expression and global language networks. We also explore how trophic levels and coherence relate to other topological properties, such as non-normality and cycle structure, and show that our method reveals the extent to which the edges in a directed network are aligned in a global direction.
Indexed as
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.