Skip to main content

2019 | OriginalPaper | Buchkapitel

10. Network Centrality: An Introduction

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Centrality is a key property of complex networks that influences the behavior of dynamical processes, like synchronization and epidemic spreading, and can bring important information about the organization of complex systems, like our brain and society. There are many metrics to quantify the node centrality in networks. Here, we review the main centrality measures and discuss their main features and limitations. The influence of network centrality on epidemic spreading and synchronization is also pointed out in this chapter. Moreover, we present the application of centrality measures to understand the function of complex systems, including biological and cortical networks. Finally, we discuss some perspectives and challenges to generalize centrality measures for multilayer and temporal networks.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Achard, S., Salvador, R., Whitcher, B., Suckling, J., & Bullmore, E. D. (2006). A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. Journal of Neuroscience, 26(1), 63–72.CrossRef Achard, S., Salvador, R., Whitcher, B., Suckling, J., & Bullmore, E. D. (2006). A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. Journal of Neuroscience, 26(1), 63–72.CrossRef
2.
Zurück zum Zitat Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., & Zhou, C. (2008). Synchronization in complex networks. Physics Reports, 469(3), 93–153.MathSciNetCrossRef Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., & Zhou, C. (2008). Synchronization in complex networks. Physics Reports, 469(3), 93–153.MathSciNetCrossRef
3.
Zurück zum Zitat Bar-Yam, Y. (1997). Dynamics of complex systems (Vol. 213). Reading: Addison-Wesley.MATH Bar-Yam, Y. (1997). Dynamics of complex systems (Vol. 213). Reading: Addison-Wesley.MATH
4.
Zurück zum Zitat Barabási, A.-L. (2016). Network science. New York: Cambridge University Press.MATH Barabási, A.-L. (2016). Network science. New York: Cambridge University Press.MATH
5.
Zurück zum Zitat Barabási, A.-L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286(5439), 509–512.MathSciNetCrossRef Barabási, A.-L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286(5439), 509–512.MathSciNetCrossRef
6.
Zurück zum Zitat Barrat, A., Barthelemy, M., & Vespignani, A. (2008). Dynamical processes on complex networks. Cambridge: Cambridge University Press.CrossRef Barrat, A., Barthelemy, M., & Vespignani, A. (2008). Dynamical processes on complex networks. Cambridge: Cambridge University Press.CrossRef
7.
Zurück zum Zitat Boccaletti, S., Bianconi, G., Criado, R., Del Genio, C. I., Gómez-Gardenes, J., Romance, M., et al. (2014). The structure and dynamics of multilayer networks. Physics Reports, 544(1), 1–122.MathSciNetCrossRef Boccaletti, S., Bianconi, G., Criado, R., Del Genio, C. I., Gómez-Gardenes, J., Romance, M., et al. (2014). The structure and dynamics of multilayer networks. Physics Reports, 544(1), 1–122.MathSciNetCrossRef
8.
Zurück zum Zitat Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., & Hwang, D.-U. (2006). Complex networks: Structure and dynamics. Physics Reports, 424(4), 175–308.MathSciNetCrossRef Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., & Hwang, D.-U. (2006). Complex networks: Structure and dynamics. Physics Reports, 424(4), 175–308.MathSciNetCrossRef
9.
Zurück zum Zitat Brandes, U. (2001). A faster algorithm for betweenness centrality. Journal of Mathematical Sociology, 25(2), 163–177.CrossRef Brandes, U. (2001). A faster algorithm for betweenness centrality. Journal of Mathematical Sociology, 25(2), 163–177.CrossRef
10.
Zurück zum Zitat Brin, S., & Page, L. (1998). The anatomy of a large-scale hypertextual web search engine. In Proceedings of the Seventh International Conference on World Wide Web 7, WWW7 (pp. 107–117). Amsterdam: Elsevier. Brin, S., & Page, L. (1998). The anatomy of a large-scale hypertextual web search engine. In Proceedings of the Seventh International Conference on World Wide Web 7, WWW7 (pp. 107–117). Amsterdam: Elsevier.
11.
Zurück zum Zitat da Fontoura Costa, L., Rodrigues, F. A., Travieso, G., & Villas Boas, P. R. (2007). Characterization of complex networks: A survey of measurements. Advances in Physics, 56(1), 167–242.CrossRef da Fontoura Costa, L., Rodrigues, F. A., Travieso, G., & Villas Boas, P. R. (2007). Characterization of complex networks: A survey of measurements. Advances in Physics, 56(1), 167–242.CrossRef
12.
Zurück zum Zitat da Fontoura Costa, L., Oliveira Jr, O. N., Travieso, G., Rodrigues, F. A., Villas Boas, P. R., Antiqueira, L., et al. (2011). Analyzing and modeling real-world phenomena with complex networks: A survey of applications. Advances in Physics, 60(3), 329–412.CrossRef da Fontoura Costa, L., Oliveira Jr, O. N., Travieso, G., Rodrigues, F. A., Villas Boas, P. R., Antiqueira, L., et al. (2011). Analyzing and modeling real-world phenomena with complex networks: A survey of applications. Advances in Physics, 60(3), 329–412.CrossRef
13.
Zurück zum Zitat de Arruda, G. F., da Fontoura Costa, L., Schubert, D., & Rodrigues, F. A. (2014). Structure and dynamics of functional networks in child-onset schizophrenia. Clinical Neurophysiology, 125(8), 1589–1595.CrossRef de Arruda, G. F., da Fontoura Costa, L., Schubert, D., & Rodrigues, F. A. (2014). Structure and dynamics of functional networks in child-onset schizophrenia. Clinical Neurophysiology, 125(8), 1589–1595.CrossRef
14.
Zurück zum Zitat De Domenico, M., Solé-Ribalta, A., Omodei, E., Gómez, S., & Arenas, A. (2013). Centrality in interconnected multilayer networks. Preprint. arXiv:1311.2906. De Domenico, M., Solé-Ribalta, A., Omodei, E., Gómez, S., & Arenas, A. (2013). Centrality in interconnected multilayer networks. Preprint. arXiv:1311.2906.
15.
Zurück zum Zitat Donges, J. F., Zou, Y., Marwan, N., & Kurths, J. (2009). The backbone of the climate network. Europhysics Letters, 87(4), 48007.CrossRef Donges, J. F., Zou, Y., Marwan, N., & Kurths, J. (2009). The backbone of the climate network. Europhysics Letters, 87(4), 48007.CrossRef
16.
Zurück zum Zitat Dorogovtsev, S. N., Goltsev, A. V., & Mendes, J. F. F. (2006). K-core organization of complex networks. Physical Review Letters, 96(4), 040601.CrossRef Dorogovtsev, S. N., Goltsev, A. V., & Mendes, J. F. F. (2006). K-core organization of complex networks. Physical Review Letters, 96(4), 040601.CrossRef
17.
Zurück zum Zitat Fagiolo, G., Reyes, J., & Schiavo, S. (2009). World-trade web: Topological properties, dynamics, and evolution. Physical Review E, 79(3), 036115.MathSciNetCrossRef Fagiolo, G., Reyes, J., & Schiavo, S. (2009). World-trade web: Topological properties, dynamics, and evolution. Physical Review E, 79(3), 036115.MathSciNetCrossRef
18.
Zurück zum Zitat Fortunato, S., & Hric, D. (2016). Community detection in networks: A user guide. Physics Reports, 659, 1–44.MathSciNetCrossRef Fortunato, S., & Hric, D. (2016). Community detection in networks: A user guide. Physics Reports, 659, 1–44.MathSciNetCrossRef
19.
Zurück zum Zitat Freeman, L. C. (1977). A set of measures of centrality based on betweenness. Sociometry, 40, 35–41.CrossRef Freeman, L. C. (1977). A set of measures of centrality based on betweenness. Sociometry, 40, 35–41.CrossRef
20.
Zurück zum Zitat Goh, K.-I., Cusick, M. E., Valle, D., Childs, B., Vidal, M., & Barabási, A.-L. (2007). The human disease network. Proceedings of the National Academy of Sciences, 104(21), 8685–8690.CrossRef Goh, K.-I., Cusick, M. E., Valle, D., Childs, B., Vidal, M., & Barabási, A.-L. (2007). The human disease network. Proceedings of the National Academy of Sciences, 104(21), 8685–8690.CrossRef
21.
Zurück zum Zitat Gómez, S., Arenas, A., Borge-Holthoefer, J., Meloni, S., & Moreno, Y. (2010). Discrete-time Markov chain approach to contact-based disease spreading in complex networks. Europhysics Letters, 89(3), 38009.CrossRef Gómez, S., Arenas, A., Borge-Holthoefer, J., Meloni, S., & Moreno, Y. (2010). Discrete-time Markov chain approach to contact-based disease spreading in complex networks. Europhysics Letters, 89(3), 38009.CrossRef
22.
Zurück zum Zitat Gómez-Gardeñes, J., Gómez, S., Arenas, A., Moreno, Y. (2011). Explosive synchronization transitions in scale-free networks. Physical Review Letters, 106(12), 128701.CrossRef Gómez-Gardeñes, J., Gómez, S., Arenas, A., Moreno, Y. (2011). Explosive synchronization transitions in scale-free networks. Physical Review Letters, 106(12), 128701.CrossRef
23.
Zurück zum Zitat Guimera, R., Mossa, S., Turtschi, A., & Amaral, L. A. N. (2005). The worldwide air transportation network: Anomalous centrality, community structure, and cities’ global roles. Proceedings of the National Academy of Sciences, 102(22), 7794–7799.MathSciNetCrossRef Guimera, R., Mossa, S., Turtschi, A., & Amaral, L. A. N. (2005). The worldwide air transportation network: Anomalous centrality, community structure, and cities’ global roles. Proceedings of the National Academy of Sciences, 102(22), 7794–7799.MathSciNetCrossRef
24.
Zurück zum Zitat Holme, P., & Saramäki, J. (2012). Temporal networks. Physics Reports, 519(3), 97–125.CrossRef Holme, P., & Saramäki, J. (2012). Temporal networks. Physics Reports, 519(3), 97–125.CrossRef
25.
Zurück zum Zitat Ichinomiya, T. (2004). Frequency synchronization in a random oscillator network. Physical Review E, 70, 026116.CrossRef Ichinomiya, T. (2004). Frequency synchronization in a random oscillator network. Physical Review E, 70, 026116.CrossRef
26.
Zurück zum Zitat Jeong, H., Mason, S. P., Barabási, A.-L., & Oltvai, Z. N. (2001). Lethality and centrality in protein networks. Nature, 411(6833), 41.CrossRef Jeong, H., Mason, S. P., Barabási, A.-L., & Oltvai, Z. N. (2001). Lethality and centrality in protein networks. Nature, 411(6833), 41.CrossRef
27.
Zurück zum Zitat Keeling, M. J., & Rohani, P. (2008). Modeling infectious diseases in humans and animals. Princeton, NJ: Princeton University Press.MATH Keeling, M. J., & Rohani, P. (2008). Modeling infectious diseases in humans and animals. Princeton, NJ: Princeton University Press.MATH
28.
Zurück zum Zitat Kitsak, M., Gallos, L. K., Havlin, S., Liljeros, F., Muchnik, L., Stanley, H. E., et al. (2010). Identification of influential spreaders in complex networks. Nature Physics, 6(11), 888.CrossRef Kitsak, M., Gallos, L. K., Havlin, S., Liljeros, F., Muchnik, L., Stanley, H. E., et al. (2010). Identification of influential spreaders in complex networks. Nature Physics, 6(11), 888.CrossRef
29.
Zurück zum Zitat Kivelä, M., Arenas, A., Barthelemy, M., Gleeson, J. P., Moreno, Y., & Porter, M. A. (2014). Multilayer networks. Journal of Complex Networks, 2(3), 203–271.CrossRef Kivelä, M., Arenas, A., Barthelemy, M., Gleeson, J. P., Moreno, Y., & Porter, M. A. (2014). Multilayer networks. Journal of Complex Networks, 2(3), 203–271.CrossRef
30.
Zurück zum Zitat Krzakala, F., Moore, C., Mossel, E., Neeman, J., Sly, A., Zdeborová, L., et al. (2013). Spectral redemption in clustering sparse networks. Proceedings of the National Academy of Sciences, 110(52), 20935–20940.MathSciNetCrossRef Krzakala, F., Moore, C., Mossel, E., Neeman, J., Sly, A., Zdeborová, L., et al. (2013). Spectral redemption in clustering sparse networks. Proceedings of the National Academy of Sciences, 110(52), 20935–20940.MathSciNetCrossRef
31.
Zurück zum Zitat Martin, T., Zhang, X., & Newman, M. E. J. (2014). Localization and centrality in networks. Physical review E, 90(5), 052808.CrossRef Martin, T., Zhang, X., & Newman, M. E. J. (2014). Localization and centrality in networks. Physical review E, 90(5), 052808.CrossRef
32.
Zurück zum Zitat Mitchell, M. (2009). Complexity: A guided tour. New York: Oxford University Press.MATH Mitchell, M. (2009). Complexity: A guided tour. New York: Oxford University Press.MATH
33.
Zurück zum Zitat Newman, M. E. J. (2013). Spectral community detection in sparse networks. Preprint. arXiv:1308.6494. Newman, M. E. J. (2013). Spectral community detection in sparse networks. Preprint. arXiv:1308.6494.
34.
Zurück zum Zitat Newman, M. E. J. (2005). A measure of betweenness centrality based on random walks. Social Networks, 27(1), 39–54.CrossRef Newman, M. E. J. (2005). A measure of betweenness centrality based on random walks. Social Networks, 27(1), 39–54.CrossRef
35.
Zurück zum Zitat Özgür, A., Vu, T., Erkan, G., & Radev, D. R. (2008). Identifying gene-disease associations using centrality on a literature mined gene-interaction network. Bioinformatics, 24(13), i277–i285.CrossRef Özgür, A., Vu, T., Erkan, G., & Radev, D. R. (2008). Identifying gene-disease associations using centrality on a literature mined gene-interaction network. Bioinformatics, 24(13), i277–i285.CrossRef
36.
Zurück zum Zitat Pastor-Satorras, R., Castellano, C., Van Mieghem, P., & Vespignani, A. (2015). Epidemic processes in complex networks. Reviews of Modern Physics, 87(3), 925.MathSciNetCrossRef Pastor-Satorras, R., Castellano, C., Van Mieghem, P., & Vespignani, A. (2015). Epidemic processes in complex networks. Reviews of Modern Physics, 87(3), 925.MathSciNetCrossRef
37.
Zurück zum Zitat Pikovsky, A., Rosenblum, M., & Kurths, J. (2003). Synchronization: A universal concept in nonlinear sciences (Vol. 12). Cambridge: Cambridge University Press.MATH Pikovsky, A., Rosenblum, M., & Kurths, J. (2003). Synchronization: A universal concept in nonlinear sciences (Vol. 12). Cambridge: Cambridge University Press.MATH
38.
Zurück zum Zitat Radicchi, F., & Castellano, C. (2016). Leveraging percolation theory to single out influential spreaders in networks. Physical Review E, 93(6), 062314.CrossRef Radicchi, F., & Castellano, C. (2016). Leveraging percolation theory to single out influential spreaders in networks. Physical Review E, 93(6), 062314.CrossRef
39.
Zurück zum Zitat Reia, S. M., Herrmann, S., & Fontanari, J. F. (2017). Impact of centrality on cooperative processes. Physical Review E, 95(2), 022305.CrossRef Reia, S. M., Herrmann, S., & Fontanari, J. F. (2017). Impact of centrality on cooperative processes. Physical Review E, 95(2), 022305.CrossRef
40.
Zurück zum Zitat Restrepo, J. G., Ott, E., & Hunt, B. R. (2005). Onset of synchronization in large networks of coupled oscillators. Physical Review E, 71, 036151.MathSciNetCrossRef Restrepo, J. G., Ott, E., & Hunt, B. R. (2005). Onset of synchronization in large networks of coupled oscillators. Physical Review E, 71, 036151.MathSciNetCrossRef
41.
Zurück zum Zitat Rodrigues, F. A., Peron, T. K. D. M., Ji, P., & Kurths, J. (2016). The Kuramoto model in complex networks. Physics Reports, 610, 1–98.MathSciNetCrossRef Rodrigues, F. A., Peron, T. K. D. M., Ji, P., & Kurths, J. (2016). The Kuramoto model in complex networks. Physics Reports, 610, 1–98.MathSciNetCrossRef
42.
Zurück zum Zitat Schultz, P., Peron, T., Eroglu, D., Stemler, T., Ramírez Ávila, G. M., Rodrigues, F. A., et al. (2016). Tweaking synchronization by connectivity modifications. Physical Review E, 93(6), 062211.CrossRef Schultz, P., Peron, T., Eroglu, D., Stemler, T., Ramírez Ávila, G. M., Rodrigues, F. A., et al. (2016). Tweaking synchronization by connectivity modifications. Physical Review E, 93(6), 062211.CrossRef
43.
Zurück zum Zitat Strogatz, S. (2004). Sync: The emerging science of spontaneous order. London: Penguin. Strogatz, S. (2004). Sync: The emerging science of spontaneous order. London: Penguin.
44.
Zurück zum Zitat Travençolo, B., & da Fontoura Costa, L. (2008). Accessibility in complex networks. Physics Letters A, 373(1), 89–95.CrossRef Travençolo, B., & da Fontoura Costa, L. (2008). Accessibility in complex networks. Physics Letters A, 373(1), 89–95.CrossRef
45.
Zurück zum Zitat Travençolo, B. A. N., Viana, M. P., & da Fontoura Costa, L. (2009). Border detection in complex networks. New Journal of Physics, 11(6), 063019.CrossRef Travençolo, B. A. N., Viana, M. P., & da Fontoura Costa, L. (2009). Border detection in complex networks. New Journal of Physics, 11(6), 063019.CrossRef
46.
Zurück zum Zitat Vogelstein, B., Lane, D., & Levine, A. J. (2000). Surfing the p53 network. Nature, 408(6810), 307–310.CrossRef Vogelstein, B., Lane, D., & Levine, A. J. (2000). Surfing the p53 network. Nature, 408(6810), 307–310.CrossRef
47.
Zurück zum Zitat Wachi, S., Yoneda, K., & Wu, R. (2005). Interactome-transcriptome analysis reveals the high centrality of genes differentially expressed in lung cancer tissues. Bioinformatics, 21(23), 4205–4208.CrossRef Wachi, S., Yoneda, K., & Wu, R. (2005). Interactome-transcriptome analysis reveals the high centrality of genes differentially expressed in lung cancer tissues. Bioinformatics, 21(23), 4205–4208.CrossRef
48.
Zurück zum Zitat Zuo, X.-N., Ehmke, R., Mennes, M., Imperati, D., Castellanos, F. X., Sporns, O., et al. (2011). Network centrality in the human functional connectome. Cerebral Cortex, 22(8), 1862–1875.CrossRef Zuo, X.-N., Ehmke, R., Mennes, M., Imperati, D., Castellanos, F. X., Sporns, O., et al. (2011). Network centrality in the human functional connectome. Cerebral Cortex, 22(8), 1862–1875.CrossRef
Metadaten
Titel
Network Centrality: An Introduction
verfasst von
Francisco Aparecido Rodrigues
Copyright-Jahr
2019
DOI
https://doi.org/10.1007/978-3-319-78512-7_10