Scilight Press

Author Information

Received: 31 Oct 2022 | Accepted: 21 Nov 2022 | Published: 22 Dec 2022

Abstract

Keywords

node centrality | biological network | network topology analysis | graph theory | biological interpretation

References 

• 1.
  Barabási, A.-L.; Oltvai, Z.N, Network Biology: Understanding the Cell’s Functional Organization. Nat Rev Genet, 2004, 5: 101−13.
• 2.
  Ma, X.; Gao, L, Biological Network Analysis: Insights into Structure and Functions. Briefings in Functional Genomics, 2012, 11: 434−42.
• 3.
  Aihara, K.; Liu, R.; Koizumi, K.; et al, Dynamical Network Biomarkers: Theory and Applications. Gene, 2022, 808: 145997.
• 4.
  Aittokallio, T.; Schwikowski, B, Graph-Based Methods for Analysing Networks in Cell Biology. Briefings in Bioinformatics, 2006, 7: 243−55.
• 5.
  Barabási, A.-L.; Gulbahce, N.; Loscalzo, J, Network Medicine: A Network-Based Approach to Human Disease. Nat Rev Genet, 2011, 12: 56−68.
• 6.
  Chen, L.; Wang, R.-S.; Zhang, X.-S. Biomolecular Networks: Methods and Applications in Systems Biology; John Wiley & Sons, 2009; ISBN 978-0-470-48805-8
• 7.
  Chin, C.-H.; Chen, S.-H.; Wu, H.-H.; et al, CytoHubba: Identifying Hub Objects and Sub-Networks from Complex Interactome. BMC Syst Biol, 2014, 8: S11.
• 8.
  Röttjers, L.; Faust, K, From Hairballs to Hypotheses–Biological Insights from Microbial Networks. FEMS Microbiology Reviews, 2018, 42: 761−80.
• 9.
  Ardaševa, A.; Doostmohammadi, A, Topological Defects in Biological Matter. Nat Rev Phys, 2022, 4: 354−6.
• 10.
  Guo, B.; Zhang, L.; Sun, H.; et al, Microbial Co-Occurrence Network Topological Properties Link with Reactor Parameters and Reveal Importance of Low-Abundance Genera. npj Biofilms Microbiomes, 2022, 8: 1−13.
• 11.
  Rashevsky, N, Topology and Life: In Search of General Mathematical Principles in Biology and Sociology. Bulletin of Mathematical Biophysics, 1954, 16: 317−48.
• 12.
  Boyd, J.W.; Neubig, R.R. Cellular Signal Transduction in Toxicology and Pharmacology: Data Collection, Analysis, and Interpretation; John Wiley & Sons, 2019; ISBN 978-1-119-06026-0
• 13.
  Jaeger, J.; Monk, N. Dynamical Modules in Metabolism, Cell and Developmental Biology. Interface Focus 11, 20210011, doi:10.1098/rsfs.2021.0011
• 14.
  Rozum, J.C.; Albert, R, Identifying (Un)Controllable Dynamical Behavior in Complex Networks. PLOS Computational Biology, 2018, 14: e1006630.
• 15.
  Hayes, B, Computing Science: Graph Theory in Practice: Part II. American Scientist, 2000, 88: 104−9.
• 16.
  Tutte, W.T.; Tutte, W.T. Graph Theory; Cambridge University Press, 2001; ISBN 978-0-521-79489-3
• 17.
  Pavlopoulos, G.A.; Secrier, M.; Moschopoulos, C.N.; et al, Using Graph Theory to Analyze Biological Networks. BioData Mining, 2011, 4: 10.
• 18.
  Assenov, Y.; Ramírez, F.; Schelhorn, S.-E.; et al, Computing Topological Parameters of Biological Networks. Bioinformatics, 2008, 24: 282−4.
• 19.
  Salau, K.R.; Baggio, J.A.; Shanafelt, D.W.; et al, Taking a Moment to Measure Networks—an Approach to Species Conservation. Landsc Ecol, 2022, 37: 2551−69.
• 20.
  del Rio, G.; Koschützki, D.; Coello, G, How to Identify Essential Genes from Molecular Networks. BMC Syst Biol, 2009, 3: 102.
• 21.
  Koutrouli, M.; Karatzas, E.; Paez-Espino, D.; et al, A Guide to Conquer the Biological Network Era Using Graph Theory. Front. Bioeng. Biotechnol., 2020, 8: 34.
• 22.
  Bihai Zhao; Jianxin Wang; Min Li; et al, Detecting Protein Complexes Based on Uncertain Graph Model. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2014, 11: 486−97.
• 23.
  Zhao, G.; Jia, P.; Huang, C.; et al, A Machine Learning Based Framework for Identifying Influential Nodes in Complex Networks. IEEE Access, 2020, 8: 65462−71.
• 24.
  Bonomo, M.; Giancarlo, R.; Greco, D.; et al, Topological Ranks Reveal Functional Knowledge Encoded in Biological Networks: A Comparative Analysis. Briefings in Bioinformatics, 2022, 23: bbac101.
• 25.
  Liu, X.; Hong, Z.; Liu, J.; et al, Computational Methods for Identifying the Critical Nodes in Biological Networks. Briefings in Bioinformatics, 2020, 21: 486−97.
• 26.
  Dablander, F.; Hinne, M, Node Centrality Measures Are a Poor Substitute for Causal Inference. Sci Rep, 2019, 9: 6846.
• 27.
  Opsahl, T.; Agneessens, F.; Skvoretz, J, Node Centrality in Weighted Networks: Generalizing Degree and Shortest Paths. Social Networks, 2010, 32: 245−51.
• 28.
  Wang, M.; Wang, H.; Zheng, H.; et al. Identifying Hub Nodes and Sub-Networks from Cattle Rumen Microbiome Multilayer Networks. In Proceedings of the Advanced Computing; Garg, D., Jagannathan, S., Gupta, A., et al., Eds.; Springer International Publishing: Cham, 2022; pp. 165–75
• 29.
  Guilbeault, D.; Centola, D, Topological Measures for Identifying and Predicting the Spread of Complex Contagions. Nat Commun, 2021, 12: 4430.
• 30.
  Ghosh, R.; Lerman, K, Parameterized Centrality Metric for Network Analysis. Phys. Rev. E, 2011, 83: 066118.
• 31.
  Hoekstra, R.H.A.; Epskamp, S.; Borsboom, D, Heterogeneity in Individual Network Analysis: Reality or Illusion. Multivariate Behavioral Research, 2022: 1−25.
• 32.
  Kaiser, T.; Jahansouz, C.; Staley, C, Network-Based Approaches for the Investigation of Microbial Community Structure and Function Using Metagenomics-Based Data. Future Microbiology, 2022, 17: 621−31.
• 33.
  Panditrao, G.; Bhowmick, R.; Meena, C.; et al, Emerging Landscape of Molecular Interaction Networks: Opportunities, Challenges and Prospects. J Biosci, 2022, 47: 24.
• 34.
  Peel, L.; Peixoto, T.P.; De Domenico, M, Statistical Inference Links Data and Theory in Network Science. Nat Commun, 2022, 13: 6794.
• 35.
  Jalili, M.; Salehzadeh-Yazdi, A.; Gupta, S.; et al, Evolution of Centrality Measurements for the Detection of Essential Proteins in Biological Networks. Front. Physiol., 2016: 7.
• 36.
  Jalili, M.; Salehzadeh-Yazdi, A.; Asgari, Y.; et al, CentiServer: A Comprehensive Resource, Web-Based Application and R Package for Centrality Analysis. PLoS One, 2015, 10: e0143111.
• 37.
  Jalili, M.; Perc, M, Information Cascades in Complex Networks. Journal of Complex Networks, 2017, 5: 665−93.
• 38.
  Rodrigues, F.A. Network Centrality: An Introduction. In A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems; Macau, E.E.N., Ed.; Nonlinear Systems and Complexity; Springer International Publishing: Cham, 2019; Vol. 22, pp. 177–96 ISBN 978-3-319-78511-0
• 39.
  Rahiminejad, S.; Maurya, M.R.; Subramaniam, S, Topological and Functional Comparison of Community Detection Algorithms in Biological Networks. BMC Bioinformatics, 2019, 20: 212.
• 40.
  Jardim, V.C.; Santos, S. de S.; Fujita, A.; et al, BioNetStat: A Tool for Biological Networks Differential Analysis. Front. Genet., 2019, 10: 594.
• 41.
  Lin, C.-Y.; Chin, C.-H.; Wu, H.-H.; et al, Hubba: Hub Objects Analyzer—a Framework of Interactome Hubs Identification for Network Biology. Nucleic Acids Research, 2008, 36: W438−43.
• 42.
  Bonacich, P, Factoring and Weighting Approaches to Status Scores and Clique Identification. The Journal of Mathematical Sociology, 1972, 2: 113−20.
• 43.
  Barthelemy, M. Spatial Networks: A Complete Introduction: From Graph Theory and Statistical Physics to Real-World Applications; Springer Nature, 2022; ISBN 978-3-030-94106-2
• 44.
  Milenković, T.; Memišević, V.; Bonato, A.; et al, Dominating Biological Networks. PLoS ONE, 2011, 6: e23016.
• 45.
  Ariya, S.S.; James, A.R.; Joseph, B, Identification of Lung Cancer Master Genes Triggered by Smoking and Their Key Pathways Based on Gene Expression Profiling. Gene Reports, 2020, 21: 100812.
• 46.
  Zhang, Y.-J.; Meng, K.; Gao, T.; et al, Analysis of Attention on Venture Capital: A Method of Complex Network on Time Series. International Journal of Modern Physics B, 2020, 34: 2050273.
• 47.
  Yu, H.; Kim, P.M.; Sprecher, E.; et al, The Importance of Bottlenecks in Protein Networks: Correlation with Gene Essentiality and Expression Dynamics. PLOS Computational Biology, 2007, 3: e59.
• 48.
  Riera-Fernández, P.; Munteanu, C.R.; Dorado, J.; et al, From Chemical Graphs in Computer-Aided Drug Design to General Markov-Galvez Indices of Drug-Target, Proteome, Drug-Parasitic Disease, Technological, and Social-Legal Networks. Curr Comput Aided Drug Des, 2011, 7: 315−37.
• 49.
  Hage, P.; Harary, F, Eccentricity and Centrality in Networks. Social Networks, 1995, 17: 57−63.
• 50.
  Valente, T.W.; Foreman, R.K, Integration and Radiality: Measuring the Extent of an Individual’s Connectedness and Reachability in a Network. Social Networks, 1998, 20: 89−105.
• 51.
  Agüero-Chapín, G.; Antunes, A.; Ubeira, F.M.; et al, Comparative Study of Topological Indices of Macro/Supramolecular RNA Complex Networks. J. Chem. Inf. Model., 2008, 48: 2265−77.
• 52.
  Checco, P.; Biey, M.; Kocarev, L, Synchronization in Random Networks with given Expected Degree Sequences. Chaos, Solitons & Fractals, 2008, 35: 562−77.
• 53.
  Lindquist, J.; Ma, J.; van den Driessche, P.; et al, Effective Degree Network Disease Models. J. Math. Biol., 2011, 62: 143−64.
• 54.
  Qian, Y.; Besenbacher, S.; Mailund, T.; et al, Identifying Disease Associated Genes by Network Propagation. BMC Syst Biol, 2014, 8: S6.
• 55.
  Kitsak, M.; Gallos, L.K.; Havlin, S.; et al, Identification of Influential Spreaders in Complex Networks. Nature Phys, 2010, 6: 888−93.
• 56.
  Piraveenan, M.; Prokopenko, M.; Hossain, L, Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks. PLOS ONE, 2013, 8: e53095.
• 57.
  Kay, B.K.; Williamson, M.P.; Sudol, M, The Importance of Being Proline: The Interaction of Proline-Rich Motifs in Signaling Proteins with Their Cognate Domains. The FASEB Journal, 2000, 14: 231−41.
• 58.
  Feng, J.; Xu, J, Identification of Pathogenic Genes and Transcription Factors in Glaucoma. Molecular Medicine Reports, 2019, 20: 216−24.
• 59.
  Yanofsky, M.F.; Ma, H.; Bowman, J.L.; et al, The Protein Encoded by the Arabidopsis Homeotic Gene Agamous Resembles Transcription Factors. Nature, 1990, 346: 35−9.
• 60.
  Bourquard, T.; Landomiel, F.; Reiter, E.; et al, Unraveling the Molecular Architecture of a G Protein-Coupled Receptor/β-Arrestin/Erk Module Complex. Sci Rep, 2015, 5: 10760.
• 61.
  Good, M.C.; Zalatan, J.G.; Lim, W.A, Scaffold Proteins: Hubs for Controlling the Flow of Cellular Information. Science, 2011, 332: 680−6.
• 62.
  Morrison, D.K.; Davis, R.J, Regulation of MAP Kinase Signaling Modules by Scaffold Proteins in Mammals. Annual Review of Cell and Developmental Biology, 2003, 19: 91−118.
• 63.
  Pawson, T.; Nash, P, Assembly of Cell Regulatory Systems Through Protein Interaction Domains. Science, 2003, 300: 445−52.
• 64.
  Aksam, V.K.M.; Chandrasekaran, V.M.; Pandurangan, S, Cancer Drug Target Identification and Node-Level Analysis of the Network of MAPK Pathways. Netw Model Anal Health Inform Bioinforma, 2018, 7: 4.
• 65.
  Cerami, E.; Demir, E.; Schultz, N.; et al, Automated Network Analysis Identifies Core Pathways in Glioblastoma. PLOS ONE, 2010, 5: e8918.
• 66.
  Kanhaiya, K.; Czeizler, E.; Gratie, C.; et al, Controlling Directed Protein Interaction Networks in Cancer. Sci Rep, 2017, 7: 10327.
• 67.
  Vinayagam, A.; Gibson, T.E.; Lee, H.-J.; et al, Controllability Analysis of the Directed Human Protein Interaction Network Identifies Disease Genes and Drug Targets. Proceedings of the National Academy of Sciences, 2016, 113: 4976−81.
• 68.
  Delprato, A, Topological and Functional Properties of the Small GTPases Protein Interaction Network. PLOS ONE, 2012, 7: e44882.
• 69.
  Jacquemet, G.; Humphries, M.J, IQGAP1 Is a Key Node within the Small GTPase Network. Small GTPases, 2013, 4: 199−207.
• 70.
  Tourette, C.; Li, B.; Bell, R.; et al, A Large Scale Huntingtin Protein Interaction Network Implicates Rho GTPase Signaling Pathways in Huntington Disease. Journal of Biological Chemistry, 2014, 289: 6709−26.
• 71.
  Zheng, W.; Zhang, J.; Song, Q.; et al, Rac Family Small GTPase 3 Correlates with Progression and Poor Prognosis in Bladder Cancer. DNA and Cell Biology, 2021, 40: 469−81.
• 72.
  Albert, R, Scale-Free Networks in Cell Biology. Journal of Cell Science, 2005, 118: 4947−57.
• 73.
  Huang, J.; Zhang, W. Analysis on Degree Distribution of Tumor Signaling Networks. 2012, 15.
• 74.
  Jenster, G, A Visualisation Concept of Dynamic Signalling Networks. Molecular and Cellular Endocrinology, 2004, 218: 1−6.
• 75.
  Teschendorff, A.E.; Banerji, C.R.S.; Severini, S.; et al, Increased Signaling Entropy in Cancer Requires the Scale-Free Property of Proteininteraction Networks. Sci Rep, 2015, 5: 9646.
• 76.
  Izudheen, S.; Mathew, S, Cancer Gene Identification Using Graph Centrality. Current Science, 2013, 105: 1143−8.
• 77.
  Yeganeh, P.N.; Saule, E.; Mostafavi, M.T. Centrality of Cancer-Related Genes in Human Biological Pathways: A Graph Analysis Perspective. In Proceedings of the 2018 IEEE International Conference on Bioinformatics and Biomedicine (BIBM); December 2018; pp. 214–8
• 78.
  Xia, J.; Sun, J.; Jia, P.; et al, Do Cancer Proteins Really Interact Strongly in the Human Protein–Protein Interaction Network. Computational Biology and Chemistry, 2011, 35: 121−5.
• 79.
  Xiong, W.; Xie, L.; Zhou, S.; et al, The Centrality of Cancer Proteins in Human Protein-Protein Interaction Network: A Revisit. International Journal of Computational Biology and Drug Design, 2014, 7: 146−56.
• 80.
  Cormen, T.H.; Leiserson, C.E.; Rivest, R.L.; et al. Introduction to Algorithms, Fourth Edition; MIT Press, 2022; ISBN 978-0-262-36750-9
• 81.
  Newman, M. Networks; Oxford University Press, 2018; Vol. 1; ISBN 978-0-19-880509-0
• 82.
  Li, C.; Xu, J, Feature Selection with the Fisher Score Followed by the Maximal Clique Centrality Algorithm Can Accurately Identify the Hub Genes of Hepatocellular Carcinoma. Sci Rep, 2019, 9: 17283.
• 83.
  Meghanathan, N. Correlation Coefficient Analysis: Centrality vs, Maximal Clique Size for Complex Real-World Network Graphs. International Journal of Network Science, 2016, 1: 3−27.
• 84.
  Evans, T.S.; Chen, B, Linking the Network Centrality Measures Closeness and Degree. Commun Phys, 2022, 5: 172.
• 85.
  Kas, M.; Carley, K.M.; Carley, L.R. Incremental Closeness Centrality for Dynamically Changing Social Networks. 2013, 9
• 86.
  Ashtiani, M.; Salehzadeh-Yazdi, A.; Razaghi-Moghadam, Z.; et al, A Systematic Survey of Centrality Measures for Protein-Protein Interaction Networks. BMC Systems Biology, 2018, 12: 80.
• 87.
  Arroyo, A.S.; Iannes, R.; Bapteste, E.; et al, Corrigendum to: Gene Similarity Networks Unveil a Potential Novel Unicellular Group Closely Related to Animals from the Tara Oceans Expedition. Genome Biol Evol, 2021, 13: evab140.
• 88.
  Mani, S.; Tlusty, T, A Topological Look into the Evolution of Developmental Programs. Biophysical Journal, 2021, 120: 4193−201.
• 89.
  Li, M.; Li, C.; Liu, W.-X.; et al, Dysfunction of PLA2G6 and CYP2C44-Associated Network Signals Imminent Carcinogenesis from Chronic Inflammation to Hepatocellular Carcinoma. J Mol Cell Biol, 2017, 9: 489−503.
• 90.
  Tang, Y.-C.; Gottlieb, A, Explainable Drug Sensitivity Prediction through Cancer Pathway Enrichment. Sci Rep, 2021, 11: 3128.
• 91.
  Zhang, J.; Wang, Y.; Shang, D.; et al, Characterizing and Optimizing Human Anticancer Drug Targets Based on Topological Properties in the Context of Biological Pathways. Journal of Biomedical Informatics, 2015, 54: 132−40.
• 92.
  Mrabet, Y.; Semmar, N, Mathematical Methods to Analysis of Topology, Functional Variability and Evolution of Metabolic Systems Based on Different Decomposition Concepts. Current Drug Metabolism, 2010, 11: 315−41.
• 93.
  Plaimas, K.; Eils, R.; König, R, Identifying Essential Genes in Bacterial Metabolic Networks with Machine Learning Methods. BMC Systems Biology, 2010, 4: 56.
• 94.
  Takemoto, K.; Niwa, T.; Taguchi, H, Difference in the Distribution Pattern of Substrate Enzymes in the Metabolic Network of Escherichia Coli, According to Chaperonin Requirement. BMC Systems Biology, 2011, 5: 98.
• 95.
  Voigt, A.; Almaas, E. Complex Network Analysis in Microbial Systems: Theory and Examples. In Microbial Systems Biology: Methods and Protocols; Navid, A., Ed.; Methods in Molecular Biology; Springer US: New York, NY, 2022; pp. 167–91 ISBN 978-1-07-161585-0
• 96.
  Chebotarev, P, The Graph Bottleneck Identity. Advances in Applied Mathematics, 2011, 47: 403−13.
• 97.
  Wu, T.; Ren, H.; Li, P.; et al. Graph Information Bottleneck. In Proceedings of the Advances in Neural Information Processing Systems; Curran Associates, Inc., 2020; Vol. 33, pp. 20437–48
• 98.
  Bima, A.; Elsamanoudy, A.; Albaqami, W.; et al, Integrative System Biology and Mathematical Modeling of Genetic Networks Identifies Shared Biomarkers for Obesity and Diabetes. Mathematical Biosciences and Engineering, 2022, 19: 2310−29.
• 99.
  Grazioli, F.; Siarheyeu, R.; Alqassem, I.; et al, Microbiome-Based Disease Prediction with Multimodal Variational Information Bottlenecks. PLOS Computational Biology, 2022, 18: e1010050.
• 100.
  Mishra, B.; Kumar, N.; Shahid Mukhtar, M, A Rice Protein Interaction Network Reveals High Centrality Nodes and Candidate Pathogen Effector Targets. Computational and Structural Biotechnology Journal, 2022, 20: 2001−12.
• 101.
  Mateus Pellenz, F.; Crispim, D.; Silveira Assmann, T, Systems Biology Approach Identifies Key Genes and Related Pathways in Childhood Obesity. Gene, 2022, 830: 146512.
• 102.
  Barthélemy, M, Betweenness Centrality in Large Complex Networks. Eur. Phys. J. B, 2004, 38: 163−8.
• 103.
  Dick, K.; Pattang, A.; Hooker, J.; et al, Human–Soybean Allergies: Elucidation of the Seed Proteome and Comprehensive Protein–Protein Interaction Prediction. J. Proteome Res., 2021, 20: 4925−47.
• 104.
  Raman, K.; Damaraju, N.; Joshi, G.K, The Organisational Structure of Protein Networks: Revisiting the Centrality–Lethality Hypothesis. Syst Synth Biol, 2014, 8: 73−81.
• 105.
  Dunn, R.; Dudbridge, F.; Sanderson, C.M, The Use of Edge-Betweenness Clustering to Investigate Biological Function in Protein Interaction Networks. BMC Bioinformatics, 2005, 6: 39.
• 106.
  Pinney, J.W.; Westhead, D.R. Betweenness-Based Decomposition Methods for Social and Biological Networks. 4
• 107.
  Narayanan, S. The Betweenness Centrality Of Biological Networks. Thesis, Virginia Tech, 2005.
• 108.
  Durón, C.; Pan, Y.; Gutmann, D.H.; et al, Variability of Betweenness Centrality and Its Effect on Identifying Essential Genes. Bull Math Biol, 2019, 81: 3655−73.
• 109.
  Sun, J.; Zhao, Z, A Comparative Study of Cancer Proteins in the Human Protein-Protein Interaction Network. BMC Genomics, 2010, 11: S5.
• 110.
  Ahmed, H.; Howton, T.C.; Sun, Y.; et al, Network Biology Discovers Pathogen Contact Points in Host Protein-Protein Interactomes. Nat Commun, 2018, 9: 2312.
• 111.
  Applied Analysis in Biological and Physical Sciences: ICMBAA, Aligarh, India, June 2015; Cushing, J.M., Saleem, M., Srivastava, H.M., et al., Eds.; Springer Proceedings in Mathematics & Statistics; Springer India: New Delhi, 2016; Vol. 186; ISBN 978-81-322-3638-2
• 112.
  Estrada, E.; Hatano, N. Resistance Distance, Information Centrality, Node Vulnerability and Vibrations in Complex Networks. In Network Science: Complexity in Nature and Technology; Estrada, E., Fox, M., Higham, D.J., et al., Eds.; Springer: London, 2010; pp. 13–29 ISBN 978-1-84996-396-1
• 113.
  Wang, Q.; Zeng, X.; Song, Q.; et al, Identification of Key Genes and Modules in Response to Cadmium Stress in Different Rice Varieties and Stem Nodes by Weighted Gene Co-Expression Network Analysis. Sci Rep, 2020, 10: 9525.
• 114.
  Pržulj, N.; Wigle, D.A.; Jurisica, I, Functional Topology in a Network of Protein Interactions. Bioinformatics, 2004, 20: 340−8.
• 115.
  Zhang, Y. New Frontiers in Graph Theory; BoD – Books on Demand, 2012; ISBN 978-953-51-0115-4
• 116.
  Krnc, M.; Sereni, J.-S.; Škrekovski, R.; et al, Eccentricity of Networks with Structural Constraints. Discuss. Math. Graph Theory, 2020, 40: 1141.
• 117.
  Takes, F.W.; Kosters, W.A, Computing the Eccentricity Distribution of Large Graphs. Algorithms, 2013, 6: 100−18.
• 118.
  Li, W.; Qiao, M.; Qin, L.; et al. Exacting Eccentricity for Small-World Networks. In Proceedings of the 2018 IEEE 34th International Conference on Data Engineering (ICDE); April 2018; pp. 785–96
• 119.
  Scardoni, G.; Petterlini, M.; Laudanna, C, Analyzing Biological Network Parameters with CentiScaPe. Bioinformatics, 2009, 25: 2857−9.
• 120.
  Zito, A.; Lualdi, M.; Granata, P.; et al, Gene Set Enrichment Analysis of Interaction Networks Weighted by Node Centrality. Frontiers in Genetics, 2021: 12.
• 121.
  Borgatti, S.P.; Everett, M.G, A Graph-Theoretic Perspective on Centrality. Social Networks, 2006, 28: 466−84.
• 122.
  Sharma, P.; Bhattacharyya, D.K.; Kalita, J.K. Centrality Analysis in PPI Networks. In Proceedings of the 2016 International Conference on Accessibility to Digital World (ICADW); December 2016; pp. 135–40
• 123.
  Khansari, M.; Kaveh, A.; Heshmati, Z.; et al. Centrality Measures for Immunization of Weighted Networks. 2016, 16
• 124.
  Currie, H.N.; Vrana, J.A.; Han, A.A.; et al, An Approach to Investigate Intracellular Protein Network Responses. Chem. Res. Toxicol., 2014, 27: 17−26.
• 125.
  Carlin, D.E.; Demchak, B.; Pratt, D.; et al, Network Propagation in the Cytoscape Cyberinfrastructure. PLoS Comput Biol, 2017, 13: e1005598.
• 126.
  Ghalmane, Z.; Cherifi, C.; Cherifi, H.; et al, Centrality in Complex Networks with Overlapping Community Structure. Sci Rep, 2019, 9: 10133.
• 127.
  Modos, D.; Brooks, J.; Fazekas, D.; et al, Identification of Critical Paralog Groups with Indispensable Roles in the Regulation of Signaling Flow. Sci Rep, 2016, 6: 38588.
• 128.
  Sabir, J.S.M.; Omri, A.E.; Shaik, N.A.; et al, Identification of Key Regulatory Genes Connected to NF-ΚB Family of Proteins in Visceral Adipose Tissues Using Gene Expression and Weighted Protein Interaction Network. PLOS ONE, 2019, 14: e0214337.
• 129.
  Zamanian-Azodi, M.; Rezaei-Tavirani, M.; Rahmati-Rad, S.; et al, Protein-Protein Interaction Network Could Reveal the Relationship between the Breast and Colon Cancer. Gastroenterol Hepatol Bed Bench, 2015, 8: 215−24.
• 130.
  Lázaro-Guevara, J.M.; Flores-Robles, B.J.; Garrido, K.; et al, Gene’s Hubs in Retinal Diseases: A Retinal Disease Network. Heliyon, 2018, 4: e00867.
• 131.
  Grando, F.; Granville, L.Z.; Lamb, L.C. Machine Learning in Network Centrality Measures: Tutorial and Outlook. ACM Comput. Surv. 2018, 51, 102:1-102:32, doi:10.1145/3237192.
• 132.
  Avella-Medina, M.; Parise, F.; Schaub, M.T.; et al, Centrality Measures for Graphons: Accounting for Uncertainty in Networks. IEEE Trans. Netw. Sci. Eng., 2020, 7: 520−37.
• 133.
  Benzi, M.; Klymko, C, On the Limiting Behavior of Parameter-Dependent Network Centrality Measures. SIAM J. Matrix Anal. & Appl., 2015, 36: 686−706.
• 134.
  Borgatti, S.P.; Carley, K.M.; Krackhardt, D, On the Robustness of Centrality Measures under Conditions of Imperfect Data. Social Networks, 2006, 28: 124−36.
• 135.
  Costenbader, E.; Valente, T.W, The Stability of Centrality Measures When Networks Are Sampled. Social Networks, 2003, 25: 283−307.
• 136.
  Segarra, S.; Ribeiro, A. Stability and Continuity of Centrality Measures in Weighted Graphs 2014
• 137.
  Grindrod, P.; Higham, D.J, A Matrix Iteration for Dynamic Network Summaries. SIAM Rev., 2013, 55: 118−28.
• 138.
  Lerman, K.; Ghosh, R.; Kang, J.H. Centrality Metric for Dynamic Networks. In Proceedings of the Proceedings of the Eighth Workshop on Mining and Learning with Graphs - MLG ’10; ACM Press: Washington, D.C., 2010; pp. 70–7
• 139.
  Pan, R.K.; Saramäki, J, Path Lengths, Correlations, and Centrality in Temporal Networks. Phys. Rev. E, 2011, 84: 016105.
• 140.
  Mendonça, M.R.F.; Barreto, A.M.S.; Ziviani, A, Approximating Network Centrality Measures Using Node Embedding and Machine Learning. IEEE Transactions on Network Science and Engineering, 2021, 8: 220−30.
• 141.
  De Domenico, M.; Solé-Ribalta, A.; Omodei, E.; et al, Ranking in Interconnected Multilayer Networks Reveals Versatile Nodes. Nat Commun, 2015, 6: 6868.
• 142.
  Qiao, T.; Shan, W.; Yu, G.; et al, A Novel Entropy-Based Centrality Approach for Identifying Vital Nodes in Weighted Networks. Entropy (Basel), 2018, 20: 261.
• 143.
  Zareie, A.; Sheikhahmadi, A.; Fatemi, A, Influential Nodes Ranking in Complex Networks: An Entropy-Based Approach. Chaos, Solitons & Fractals, 2017, 104: 485−94.