ArticleProceedings of the National Academy of Sciences of the United States of America2013
On the origins of hierarchy in complex networks.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 45 papers.
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Who cites it
45 citing papers in PubMed, 162 citations in OpenAlex.
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- Can the Timing of the Origin of Life Be Inferred from Trends in the Growth of Organismal Complexity?Life (Basel, Switzerland) · 2026Article
- A simulated annealing algorithm for randomizing weighted networks.Nature computational science · 2025Article
- Fundamental constraints to the logic of living systems.Interface focus · 2024Review
- Self-complexification through integral feedback in eusocial paper wasps of various levels of sociality.Heliyon · 2023Article
- Internal control of brain networks via sparse feedback.AIChE journal. American Institute of Chemical Engineers · 2023Article
- FLONE: fully Lorentz network embedding for inferring novel drug targets.Bioinformatics advances · 2023Article
- Facilitative interaction networks in experimental microbial community dynamics.Frontiers in microbiology · 2023Article
- Evolving collaboration, dependencies, and use in the Rust Open Source Software ecosystem.Scientific data · 2022Article
- Neural network organization for courtship-song feature detection in Drosophila.Current biology : CB · 2022Article
- Evolution of Brains and Computers: The Roads Not Taken.Entropy (Basel, Switzerland) · 2022Article
- The rise of hierarchy and modularity in biological networks explained by empedocles' double tale ∼2,400 years before darwin and systems biology.Frontiers in genetics · 2022Article
- Graph hierarchy: a novel framework to analyse hierarchical structures in complex networks.Scientific reports · 2021Article
- A morphospace of functional configuration to assess configural breadth based on brain functional networks.Network neuroscience (Cambridge, Mass.) · 2021Article
- How directed is a directed network?Royal Society open science · 2020Article
- Fate of Duplicated Neural Structures.Entropy (Basel, Switzerland) · 2020Review
- Construction, comparison and evolution of networks in life sciences and other disciplines.Journal of the Royal Society, Interface · 2020Article
- Evolving complexity: how tinkering shapes cells, software and ecological networks.Philosophical transactions of the Royal Society of London. Series B, Biological sciences · 2020Article
- Keystone Species and Modularity in Microbial Hydrocarbon Degradation Uncovered by Network Analysis and Association Rule Mining.Microorganisms · 2020Article
Corrections and comments
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Authors and funding
4 authors at 3 institutions in 3 countries.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Hierarchy seems to pervade complexity in both living and artificial systems. Despite its relevance, no general theory that captures all features of hierarchy and its origins has been proposed yet. Here we present a formal approach resulting from the convergence of theoretical morphology and network theory that allows constructing a 3D morphospace of hierarchies and hence comparing the hierarchical organization of ecological, cellular, technological, and social networks. Embedded within large voids in the morphospace of all possible hierarchies, four major groups are identified. Two of them match the expected from random networks with similar connectivity, thus suggesting that nonadaptive factors are at work. Ecological and gene networks define the other two, indicating that their topological order is the result of functional constraints. These results are consistent with an exploration of the morphospace, using in silico evolved networks.
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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.