{"doi":"10.1038/ncomms3447","title":"Exact controllability of complex networks","abstract":null,"journal":"Nature Communications","year":2013,"id":648981,"datarank":0.9536763399762151,"base_score":6.3578422665081,"endowment":6.3578422665081,"self_citation_contribution":0.9536763399762151,"citation_network_contribution":0.0,"self_endowment_contribution":0.9536763399762151,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":576,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1427392,"name":"Chen Zhao","orcid":"0000-0003-4226-7793","position":1,"is_corresponding":false},{"id":1618408,"name":"Zengru Di","orcid":null,"position":2,"is_corresponding":false},{"id":1691583,"name":"Wen-Xu Wang","orcid":null,"position":3,"is_corresponding":false},{"id":1691586,"name":"Ying-Cheng Lai","orcid":null,"position":4,"is_corresponding":false},{"id":1691582,"name":"Zhengzhong Yuan","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"resolved":true,"title":"Exact controllability of complex networks","abstract":"Controlling complex networks is of paramount importance in science and engineering. Despite the recent development of structural controllability theory, we continue to lack a framework to control undirected complex networks, especially given link weights. Here we introduce an exact controllability paradigm based on the maximum multiplicity to identify the minimum set of driver nodes required to achieve full control of networks with arbitrary structures and link-weight distributions. The framework reproduces the structural controllability of directed networks characterized by structural matrices. We explore the controllability of a large number of real and model networks, finding that dense networks with identical weights are difficult to be controlled. An efficient and accurate tool is offered to assess the controllability of large sparse and dense networks. The exact controllability framework enables a comprehensive understanding of the impact of network properties on controllability, a fundamental problem towards our ultimate control of complex systems. Although it has been possible to calculate the conditions for exerting complete control over a directed complex network, for undirected and weighted networks this calculation is inexact. Yuan et al. develop a general framework for determining the controllability of any complex network.","is_dataset_classified":null,"base_score":6.3578422665081,"endowment":6.3578422665081,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"24025746","pmcid":"PMC3945876","openalex_id":"https://openalex.org/W1982821381","authors":[],"funders":[{"funder_name":"National Science Foundation","grant_id":"1026710","title":"CDI-Type I: Data-Based Prediction of Complex Networks and Applications"},{"funder_name":"National Science Foundation","grant_id":"1023101","title":"Control, Design and Optimization of Complex Networked Systems"}],"total_grants":2,"fwci":34.5806,"citation_percentile":0.99916716,"influential_citations":0,"citation_trend":[{"year":2013,"count":3},{"year":2014,"count":32},{"year":2015,"count":51},{"year":2016,"count":65},{"year":2017,"count":52},{"year":2018,"count":56},{"year":2019,"count":57},{"year":2020,"count":50},{"year":2021,"count":37},{"year":2022,"count":42},{"year":2023,"count":43},{"year":2024,"count":52},{"year":2025,"count":26},{"year":2026,"count":10}],"oa_status":"hybrid","license":"cc-by-nc-sa","oa_locations":[{"url":"https://www.nature.com/articles/ncomms3447.pdf","host_type":"journal"},{"url":"https://www.nature.com/articles/ncomms3447.pdf","host_type":"publisher"},{"url":"http://www.nature.com/articles/ncomms3447.pdf","host_type":"publisher"},{"url":"http://www.nature.com/articles/ncomms3447","host_type":"publisher"},{"url":"https://doi.org/10.1038/ncomms3447","host_type":"journal"},{"url":"https://pubmed.ncbi.nlm.nih.gov/24025746","host_type":"repository"},{"url":"http://arxiv.org/abs/1310.5806","host_type":"repository"},{"url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.379.2397","host_type":""},{"url":"https://www.nature.com/articles/ncomms3447","host_type":"repository"},{"url":"http://europepmc.org/articles/PMC3945876","host_type":"repository"},{"url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3945876","host_type":"repository"},{"url":"https://arxiv.org/pdf/1310.5806","host_type":"repository"},{"url":"https://europepmc.org/articles/PMC3945876","host_type":"Europe_PMC"},{"url":"https://europepmc.org/articles/PMC3945876?pdf=render","host_type":"Europe_PMC"},{"url":"https://dx.doi.org/10.48550/arxiv.1310.5806","host_type":""},{"url":"http://dx.doi.org/10.1038/ncomms3447","host_type":""},{"url":"https://dx.doi.org/10.1038/ncomms3447","host_type":""}],"fields_of_study":["Complex Network Analysis Techniques","Opinion Dynamics and Social Influence","Neural Networks Stability and Synchronization","0301 basic medicine","03 medical and health sciences","0209 industrial biotechnology","02 engineering and technology"],"mesh_terms":[],"keywords":["Controllability","Network controllability","Complex network","Computer science","Complex system","Set (abstract data type)","Control (management)","Topology (electrical circuits)","Distributed computing","Mathematics","Centrality","Artificial intelligence","Betweenness centrality","Applied mathematics","Social and Information Networks (cs.SI)","FOS: Computer and information sciences","Physics - Physics and Society","FOS: Physical sciences","Computer Science - Social and Information Networks","Physics and Society (physics.soc-ph)","Disordered Systems and Neural Networks (cond-mat.dis-nn)","Condensed Matter - Disordered Systems and Neural Networks","Article"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-08-10T03:10:50.500830Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}