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Disentangling direct from indirect relationships in association networks

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Connected Components in Random Graphs with Given Expected Degree Sequences

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Microarray analysis of RpoS-mediated gene expression in Escherichia coli K-12

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Causality, cointegration, and control

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Indirect effects in community ecology: Their definition, study and importance

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Computational inference of gene regulatory networks: Approaches, limitations and opportunities

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Gene regulatory network inference: Data integration in dynamic models—A review

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Disentangling Interactions in the Microbiome: A Network Perspective

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A matrix partial correlation test used in investigations of reciprocity and other social interaction patterns at group level

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A bivariate causality between stock prices and exchange rates: evidence from recent Asianflu☆

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Hierarchical structure and the prediction of missing links in networks

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Indirect effects drive coevolution in mutualistic networks

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Network link prediction by global silencing of indirect correlations

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Network deconvolution as a general method to distinguish direct dependencies in networks

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Network cleanup

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Wisdom of crowds for robust gene network inference

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Classes of complex networks defined by role-to-role connectivity profiles

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Network biology: understanding the cell's functional organization

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Biological robustness

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Advantages and limitations of current network inference methods

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Climate warming leads to divergent succession of grassland microbial communities

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Climate warming enhances microbial network complexity and stability

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Climate warming accelerates temporal scaling of grassland soil microbial biodiversity

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Inferring sparse networks for noisy transient processes

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Network structure and biodiversity loss in food webs: robustness increases with connectance

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The modularity of pollination networks

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Revealing strengths and weaknesses of methods for gene network inference

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Discriminating direct and indirect connectivities in biological networks

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Part mutual information for quantifying direct associations in networks

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Breakdown of interdependent directed networks

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Using Bayesian Networks to Analyze Expression Data

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Discovery of meaningful associations in genomic data using partial correlation coefficients

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Inferring gene regulatory networks from gene expression data by path consistency algorithm based on conditional mutual information

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Inferring gene regulatory networks by ANOVA

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A field guide for the compositional analysis of any-omics data

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Adaptation in bacterial flagellar and motility systems: from regulon members to ‘foraging’-like behavior in E. coli

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RegulonDB version 9.0: high-level integration of gene regulation, coexpression, motif clustering and beyond

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Transcription profile of Escherichia coli : genomic SELEX search for regulatory targets of transcription factors

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The EcoCyc database: reflecting new knowledge aboutEscherichia coliK-12

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A sigma factor toolbox for orthogonal gene expression in Escherichia coli

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RegulonDB v 10.5: tackling challenges to unify classic and high throughput knowledge of gene regulation inE. coliK-12

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Finding community structure in networks using the eigenvectors of matrices

inferredcites →https://doi.org/10.1126/science.1065103openalex-snapshot

Specificity and Stability in Topology of Protein Networks

inferredcites →https://doi.org/10.1126/science.1089072openalex-snapshot

Biological Networks: The Tinkerer as an Engineer

inferredcites →https://doi.org/10.1126/science.aah3449openalex-snapshot

Network analytics in the age of big data

inferredcites →https://doi.org/10.1126/science.aal4122openalex-snapshot

Effects of network modularity on the spread of perturbation impact in experimental metapopulations

inferredcites →https://doi.org/10.1126/science.aan8075openalex-snapshot

The importance of being modular

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Genome-Wide Analysis of the General Stress Response Network in Escherichia coli : σ S -Dependent Genes, Promoters, and Sigma Factor Selectivity

inferredcites →https://doi.org/10.1128/mbio.00122-11openalex-snapshot

Phylogenetic Molecular Ecological Network of Soil Microbial Communities in Response to Elevated CO 2

inferredcites →https://doi.org/10.1128/mbio.00169-10openalex-snapshot

Functional Molecular Ecological Networks

inferredcites →https://doi.org/10.1128/mbio.02352-14openalex-snapshot

BolA Is a Transcriptional Switch That Turns Off Motility and Turns On Biofilm Development

inferredcites →https://doi.org/10.1137/1.9780898717921openalex-snapshot

Inverse Problem Theory and Methods for Model Parameter Estimation

inferredcites →https://doi.org/10.1186/1471-2105-13-113openalex-snapshot

Molecular ecological network analyses

inferredcites →https://doi.org/10.1186/1471-2164-14-745openalex-snapshot

RegPrecise 3.0 – A resource for genome-scale exploration of transcriptional regulation in bacteria

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Eigengene networks for studying the relationships between co-expression modules

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Dialogue on Reverse‐Engineering Assessment and Methods

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Linkage Rules for Plant–Pollinator Networks: Trait Complementarity or Exploitation Barriers?

inferredcites →https://doi.org/10.1371/journal.pcbi.1000117openalex-snapshot

Geometric Interpretation of Gene Coexpression Network Analysis

inferredcites →https://doi.org/10.1371/journal.pcbi.1004226openalex-snapshot

Sparse and Compositionally Robust Inference of Microbial Ecological Networks

inferredcites →https://doi.org/10.1371/journal.pgen.1004649openalex-snapshot

Comprehensive Mapping of the Escherichia coli Flagellar Regulatory Network

inferredcites →https://doi.org/10.1371/journal.pone.0179181openalex-snapshot

The whole set of the constitutive promoters recognized by four minor sigma subunits of Escherichia coli RNA polymerase

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On the Interpretation of χ 2 from Contingency Tables, and the Calculation of P

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Deciphering microbial interactions and detecting keystone species with co-occurrence networks

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inferred← citeshttps://doi.org/10.1016/j.rhisph.2024.100972openalex-snapshot

Revealing the characteristics of myxobacterial communities in rhizosphere and non-rhizosphere soils of halophytic plants following wetland degradation using high-throughput sequencing

inferred← citeshttps://doi.org/10.1016/j.scitotenv.2022.159311openalex-snapshot

Co-composting of faecal sludge and carbon-rich wastes in the earthworm's synergistic cooperation system: Performance, global warming potential and key microbiome

inferred← citeshttps://doi.org/10.1016/j.scitotenv.2022.160418openalex-snapshot

Habitats modulate influencing factors shaping the spatial distribution of bacterial communities along a Tibetan Plateau riverine wetland

inferred← citeshttps://doi.org/10.1016/j.scitotenv.2023.169568openalex-snapshot

Unveiling the power of COD/N on constructed wetlands in a short-term experiment: Exploring microbiota co-occurrence patterns and assembly dynamics

inferred← citeshttps://doi.org/10.1016/j.scitotenv.2024.169975openalex-snapshot

Communication mediated interaction between bacteria and microalgae advances photogranulation

inferred← citeshttps://doi.org/10.1016/j.scitotenv.2024.169976openalex-snapshot

Polysaccharide preferred minority-dominant community assembly and exoenzyme enrichment in transparent exopolymer particles: Implication for global carbon cycle in water

inferred← citeshttps://doi.org/10.1016/j.scitotenv.2024.172724openalex-snapshot

Impact of grassland degradation on soil multifunctionality: Linking to protozoan network complexity and stability

inferred← citeshttps://doi.org/10.1016/j.scitotenv.2024.173007openalex-snapshot

Insights into the response mechanisms of activated sludge system under long-term dexamethasone stress

inferred← citeshttps://doi.org/10.1016/j.scitotenv.2024.175228openalex-snapshot

Dynamic responses of soil microbial communities to seasonal freeze-thaw cycles in a temperate agroecosystem

inferred← citeshttps://doi.org/10.1016/j.scitotenv.2025.178413openalex-snapshot

Recruitment of specific rhizosphere microorganisms in saline-alkali tolerant rice improves adaptation to saline-alkali stress

inferred← citeshttps://doi.org/10.1016/j.soilbio.2024.109560openalex-snapshot

Multiple anthropogenic environmental stressors structure soil bacterial diversity and community network

inferred← citeshttps://doi.org/10.1016/j.soilbio.2025.109893openalex-snapshot

Drought has short-term effects on soil fungal communities leading to long-term effects on soil functions

inferred← citeshttps://doi.org/10.1016/j.tim.2025.01.013openalex-snapshot

Disentangling microbial interaction networks

inferred← citeshttps://doi.org/10.1016/j.watres.2022.119270openalex-snapshot

Microbial fingerprints of methanation in a hybrid electric-biological anaerobic digestion

inferred← citeshttps://doi.org/10.1016/j.watres.2023.120524openalex-snapshot

Effects of ammonia nitrogen and organic carbon availability on microbial community structure and ecological interactions in a full-scale partial nitritation and anammox (PN/A) system

inferred← citeshttps://doi.org/10.1016/j.watres.2024.121600openalex-snapshot

New insights into substrates shaped nutrients removal, species interactions and community assembly mechanisms in tidal flow constructed wetlands treating low carbon-to-nitrogen rural wastewater

inferred← citeshttps://doi.org/10.1016/j.watres.2024.122239openalex-snapshot

High biological N fixation potential dominated by heterotrophic diazotrophs in alpine permafrost rivers on the Qinghai‒Tibet Plateau

inferred← citeshttps://doi.org/10.1016/j.watres.2025.123419openalex-snapshot

Micron-scale heterogeneity reduction leads to increased interspecies competition in thermophilic digestion microbiome

inferred← citeshttps://doi.org/10.1016/j.watres.2026.126624openalex-snapshot

Artificial intelligence-assisted phenotypic monitoring and diagnostic of wastewater microbiome management towards sustainability

inferred← citeshttps://doi.org/10.1016/j.yebeh.2024.110144openalex-snapshot

Drug-resistant epilepsy: Is there an overlooked association between drug resistant epilepsies and neuropsychiatric comorbidities?

inferred← citeshttps://doi.org/10.1021/acs.est.3c01899openalex-snapshot

Adaptive Evolution Laws of Biofilm under Emerging Pollutant-Induced Stress: Community Assembly-Driven Structure Response

inferred← citeshttps://doi.org/10.1021/acs.est.3c05452openalex-snapshot

Enhanced Bacterium–Phage Symbiosis in Attached Microbial Aggregates on a Membrane Surface Facing Elevated Hydraulic Stress

inferred← citeshttps://doi.org/10.1021/acs.est.5c00490openalex-snapshot

Bacterium–Phage Interactions Enhance Biofilm Resilience during Membrane Filtration Biofouling under Oxidative and Hydraulic Stresses

inferred← citeshttps://doi.org/10.1021/acs.est.5c15228openalex-snapshot

Spatial Organization of Microbiome Stability and Nitrogen Removal Resilience in a Full-Scale Plug-Flow PN/A System

inferred← citeshttps://doi.org/10.1021/acsestengg.3c00008openalex-snapshot

Influent Disturbance Drives Microbial Assembly Pattern and Co-occurrence Network, Linking to the Operating Performance in Full-Scale Leachate Anoxic/Aerobic Process

inferred← citeshttps://doi.org/10.1029/2024jg008723openalex-snapshot

Lake State Shifts After Earthquakes in Tectonically Active Regions

inferred← citeshttps://doi.org/10.1038/s41396-023-01521-xopenalex-snapshot

Land use conversion increases network complexity and stability of soil microbial communities in a temperate grassland

inferred← citeshttps://doi.org/10.1038/s41558-024-02101-3openalex-snapshot

Plant–microbe interactions underpin contrasting enzymatic responses to wetland drainage

inferred← citeshttps://doi.org/10.1063/5.0087607openalex-snapshot

Partial event coincidence analysis for distinguishing direct and indirect coupling in functional network construction

inferred← citeshttps://doi.org/10.1073/pnas.2303568120openalex-snapshot

Multidisciplinary learning through collective performance favors decentralization

inferred← citeshttps://doi.org/10.1073/pnas.2537753123openalex-snapshot

Experimental drought drives divergent succession of soil microbiota

inferred← citeshttps://doi.org/10.1093/bib/bbac241openalex-snapshot

Associating pathways with diseases using single-cell expression profiles and making inferences about potential drugs

inferred← citeshttps://doi.org/10.1093/bioinformatics/btae435openalex-snapshot

Reverse network diffusion to remove indirect noise for better inference of gene regulatory networks

inferred← citeshttps://doi.org/10.1093/bioinformatics/btag738openalex-snapshot

METANet: a supervised ensemble learning framework for reconstructing direct and functional tissue-specific transcription factor networks

inferred← citeshttps://doi.org/10.1093/femsec/fiad166openalex-snapshot

Microcystis blooms caused the decreasing richness of and interactions between free-living microbial functional genes in Lake Taihu, China

inferred← citeshttps://doi.org/10.1093/femsmc/xtae028openalex-snapshot

Size fractionation informs microbial community composition and interactions in the eastern tropical North Pacific Ocean

inferred← citeshttps://doi.org/10.1093/ismeco/ycae152openalex-snapshot

Warming stimulates cellulose decomposition by recruiting phylogenetically diverse but functionally similar microorganisms

inferred← citeshttps://doi.org/10.1093/ismejo/wraf118openalex-snapshot

Climate warming enhances biodiversity and stability of grassland soil phosphorus-cycling microbial communities

inferred← citeshttps://doi.org/10.1093/ismejo/wraf191openalex-snapshot

Multi-scale evidence for declining microbial carbon fixation along forest succession gradients

inferred← citeshttps://doi.org/10.1093/jpe/rtaf125openalex-snapshot

Effects of mixed cultivation of Larix gmelinii and Juglans mandshurica on the adaptive strategies of fine roots and root-associated fungi

inferred← citeshttps://doi.org/10.1101/2023.09.10.556351openalex-snapshot

ENQUIRE RECONSTRUCTS AND EXPANDS CONTEXT-SPECIFIC CO-OCCURRENCE NETWORKS FROM BIOMEDICAL LITERATURE

inferred← citeshttps://doi.org/10.1101/2025.11.14.688560openalex-snapshot

Consistent drought regulation in grapevine is driven by directional transcription factor activity

inferred← citeshttps://doi.org/10.1109/bibm55620.2022.9994884openalex-snapshot

Refinement of Biological Regulatory Graphs using Functional Enrichment

inferred← citeshttps://doi.org/10.1109/case56687.2023.10260446openalex-snapshot

A Framework of Direct Correlation Identification for Wafer Fault Detection

inferred← citeshttps://doi.org/10.1109/icamal62577.2024.10919718openalex-snapshot

Deviation Propagation Network for Key Quality Factors Identification of Complex Assembly Systems

inferred← citeshttps://doi.org/10.1109/ieem58616.2023.10406564openalex-snapshot

An Influential Node Identification Framework in the Aircraft Assembly Network Based on the Community Structure

inferred← citeshttps://doi.org/10.1109/jbhi.2025.3628564openalex-snapshot

TransGRN: A Transfer Learning-Based Framework for Inferring Gene Regulatory Networks Across Cell Lines

inferred← citeshttps://doi.org/10.1109/jbhi.2026.3674779openalex-snapshot

SPSID: A Single-Parameter Shrinkage Inverse-Diffusion for Denoising Gene-Regulatory Networks

inferred← citeshttps://doi.org/10.1109/tem.2024.3399758openalex-snapshot

Measuring the Global Digital Technology Innovation Network in the Construction Industry

inferred← citeshttps://doi.org/10.1111/1462-2920.16388openalex-snapshot

Bacterial inoculation of Quercus pyrenaica trees alters co‐occurrence patterns but not the composition of the rhizosphere bacteriome in wild conditions

inferred← citeshttps://doi.org/10.1111/mec.70205openalex-snapshot

Contrasting Lifestyle of Free‐Living and Particle‐Attached Microbes Shaped Community Dynamics and Stability in the Seamount Environment

inferred← citeshttps://doi.org/10.1111/mec.70277openalex-snapshot

Niche Overlap of Soil Bacteria Drives Stress Gradient Hypothesis Dynamics in Dryland Biocrust Succession

inferred← citeshttps://doi.org/10.1111/pce.15350openalex-snapshot

Microbial Biotic Associations Dominated Adaptability Differences of Dioecious Poplar Under Salt Stress

inferred← citeshttps://doi.org/10.1128/aem.00448-26openalex-snapshot

A horizontal connectivity mode in coastal oceans: transport overrides stratification to govern microbiome network stability

inferred← citeshttps://doi.org/10.1128/mbio.03535-22openalex-snapshot

Niche Modification by Sulfate-Reducing Bacteria Drives Microbial Community Assembly in Anoxic Marine Sediments

inferred← citeshttps://doi.org/10.1128/msphere.00395-24openalex-snapshot

Community organization and network complexity and stability: contrasting strategies of prokaryotic versus eukaryotic microbiomes in the Bohai Sea and Yellow Sea

inferred← citeshttps://doi.org/10.1128/msphere.00607-23openalex-snapshot

Taxonomic and functional assembly cues enrich the endophytic tobacco microbiota across epiphytic compartments

inferred← citeshttps://doi.org/10.1128/msystems.00002-23openalex-snapshot

Kelp Culture Enhances Coastal Biogeochemical Cycles by Maintaining Bacterioplankton Richness and Regulating Its Interactions

inferred← citeshttps://doi.org/10.1128/spectrum.01051-24openalex-snapshot

Assembly process and co-occurrence network of microbial community in response to free ammonia gradient distribution

inferred← citeshttps://doi.org/10.1128/spectrum.02026-23openalex-snapshot

Temporal approach to identifying ectomycorrhizal community associated with Mongolian pine in a desert environment, northern China

inferred← citeshttps://doi.org/10.1128/spectrum.02182-24openalex-snapshot

Gut mycobiome alterations and network interactions with the bacteriome in patients with atherosclerotic cardiovascular disease

inferred← citeshttps://doi.org/10.1128/spectrum.04371-22openalex-snapshot

Distinctive Structure and Assembly of Phyllosphere Microbial Communities between Wild and Cultivated Rice

inferred← citeshttps://doi.org/10.1186/s12866-025-04348-yopenalex-snapshot

Characterization of the gut mycobiome in patients with non-alcoholic fatty liver disease and correlations with serum metabolome

inferred← citeshttps://doi.org/10.1186/s12870-026-08391-3openalex-snapshot

Properties and ecological assembly mechanisms of microbial communities across salinity levels in coastal saline-alkaline soils

inferred← citeshttps://doi.org/10.1186/s12967-025-07423-0openalex-snapshot

Altered gut mycobiome and cross-kingdom microbial interactions in systemic lupus erythematosus

inferred← citeshttps://doi.org/10.1186/s40168-024-01883-0openalex-snapshot

Deciphering the role of rhizosphere microbiota in modulating disease resistance in cabbage varieties

inferred← citeshttps://doi.org/10.1186/s40168-024-01965-zopenalex-snapshot

From grasslands to genes: exploring the major microbial drivers of antibiotic-resistance in microhabitats under persistent overgrazing

inferred← citeshttps://doi.org/10.1186/s40168-024-01989-5openalex-snapshot

Asymmetric succession in soil microbial communities enhances the competitive advantage of invasive alien plants

inferred← citeshttps://doi.org/10.1186/s40168-025-02216-5openalex-snapshot

Unveiling essential host genes and keystone microorganisms of the olive tree holobiont linked to Verticillium wilt tolerance

inferred← citeshttps://doi.org/10.1186/s40793-023-00516-7openalex-snapshot

Modules in robust but low-efficiency phyllosphere fungal networks drive saponin accumulation in leaves of different Panax species

inferred← citeshttps://doi.org/10.1186/s40793-025-00821-3openalex-snapshot

The microbial community metabolic regime adapts to hydraulic disturbance in river–lake systems with high–frequency regulation

inferred← citeshttps://doi.org/10.1371/journal.pcbi.1012745openalex-snapshot

ENQUIRE automatically reconstructs, expands, and drives enrichment analysis of gene and Mesh co-occurrence networks from context-specific biomedical literature

inferred← citeshttps://doi.org/10.21203/rs.3.rs-2541271/v1openalex-snapshot

A healthier microbiome helps transgenic maize to defend herbicide toxicity

inferred← citeshttps://doi.org/10.21203/rs.3.rs-2893383/v1openalex-snapshot

Distinct microbiota assembly and functional patterns revealed by comparative analysis of disease resistant and susceptible tobacco (Nicotiana tabacum) varieties

inferred← citeshttps://doi.org/10.21203/rs.3.rs-3281696/v1openalex-snapshot

Linking root-associated fungal communities, wheat evolutionary patterns, and productivity: overlooked roles of rare taxa

inferred← citeshttps://doi.org/10.2139/ssrn.5340292openalex-snapshot

No2- and S0 Accumulation Mechanisms in Double Short-Cut Sulfur Autotrophic Denitrification System Under Ammonia Stress

inferred← citeshttps://doi.org/10.3389/fevo.2024.1343672openalex-snapshot

Composition and diversity of rhizosphere microorganisms of Suaeda salsa in the Yellow River Delta

inferred← citeshttps://doi.org/10.3389/fmicb.2023.1095688openalex-snapshot

The shift of soil microbial community induced by cropping sequence affect soil properties and crop yield

inferred← citeshttps://doi.org/10.3389/fmicb.2023.1109128openalex-snapshot

Grass-microbial inter-domain ecological networks associated with alpine grassland productivity

inferred← citeshttps://doi.org/10.3389/fmicb.2023.1264619openalex-snapshot

Effects of long-term metal exposure on the structure and co-occurrence patterns of the oral microbiota of residents around a mining area

inferred← citeshttps://doi.org/10.3389/fmicb.2025.1633687openalex-snapshot

Succession characteristics and assembly process of soil microbiome at reclaimed farmlands in coal mining area

inferred← citeshttps://doi.org/10.3389/fpls.2023.1194598openalex-snapshot

Differences in rhizosphere soil fungal communities of wild and cultivated Paeonia ludlowii species

inferred← citeshttps://doi.org/10.3390/biology13121022openalex-snapshot

Antibiotic Resistance as a Functional Characteristic of Urban Dust Particles’ Microbial Communities

inferred← citeshttps://doi.org/10.3390/biom15111578openalex-snapshot

From Lab to Field: Context-Dependent Impacts of Pseudomonas-Produced 2,4-Diacetylphloroglucinol on Soil Microbial Ecology

inferred← citeshttps://doi.org/10.3390/microorganisms11010064openalex-snapshot

Long-Term Manure Amendment Sustains Black Soil Biodiversity by Mitigating Acidification Induced by Chemical N Fertilization

inferred← citeshttps://doi.org/10.3390/microorganisms14071387openalex-snapshot

Stage-Dependent Dynamics and Assembly Processes of PhoD-Harboring Bacterial Communities Driven by Ulva prolifera Green Tides

inferred← citeshttps://doi.org/10.3390/w16213155openalex-snapshot

Benthic Microbes on the Shore of Southern Lake Taihu Exhibit Ecological Significance and Toxin-Producing Potential Through Comparison with Planktonic Microbes

inferred← citeshttps://doi.org/10.6084/m9.figshare.26603770openalex-snapshot

Additional file 1 of Modules in robust but low-efficiency phyllosphere fungal networks drive saponin accumulation in leaves of different Panax species

inferred← citeshttps://doi.org/10.7498/aps.73.20240334openalex-snapshot

Reconstruction of simplex structures based on phase synchronization dynamics

inferred← citeshttps://doi.org/10.7744/kjoas.510440openalex-snapshot

Characteristics of endophytic bacteria in Cnidium officinale Makino from the Republic of Korea

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