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Towards an Information Theory of Complex Networks pp 199–258Cite as

Birkhäuser

Markov Entropy Centrality: Chemical, Biological, Crime, and Legislative Networks

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Abstract

In this chapter, we propose the study of multiple systems using node centrality or connectedness information measures derived from a Graph or Complex Network. The information is quantified in terms of the Entropy centrality kC θ(j) of the jth parts or states (nodes) of a Markov Chain associated with the system, represented by a network graph. The procedure is standard for all systems despite the complexity of the system. First, we define the phenomena to study, ranging from molecular systems composed by single molecules (drug activity, drug toxicity), multiple molecules (networks of chemical reactions), and macromolecules (DNA–drug interaction, protein function), to ecological systems (bacterial co-aggregation), or social systems (criminal causation, legislative productivity). Second, we collect several cases from literature (drugs, chemical reactions, proteins, bacterial species, or criminal cases). Next, we classify the cases in at least two different groups (active/nonactive drugs, enantioselective/non-enantioselective reactions, functional/nonfunctional proteins, co-aggregating/non-co-aggregating bacteria, or crime/noncrime cause, efficient/nonefficient law). After that, we represent the interconnectivity of the discrete parts of the system (atoms, amino acids, reactants, bacteria species, or people) as a graph or network. The Markov Chain theory is used to calculate the entropy of the system for nodes placed at different distances. Finally, we aim to both derive and validate a classification model using the entropy values as input variables and the classification of cases as the output variables. The model is used to predict the probability with which a case presents the studied property. The present work proposes the entropy of a Markov Chain associated with a network or graph to be used as a universal quantity in pattern recognition regardless the chemical, biological, social, or other nature of the systems under study.

MSC2000 Primary 57Q05; Secondary 37B40, 68R10, 65C40, 91D30.

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Acknowledgements

C.R. Munteanu and H. González-Díaz acknowledge financial support of Program Isidro Parga Pondal of the funded by Dirección Xeral de Investigación e Desenvolvemento, Xunta de Galicia. S. Arrasate acknowledges sponsorships for a tenure-track research position at the University of Santiago de Compostela from the “Ikertzaileak Hobetzeko eta Mugitzeko/Perfeccionamiento y Movilidad del Personal Investigador” Program of the “Hezkuntza, Unibertsitate eta Ikerketa Saila/Departamento de Educación, Universidades e Investigación, Eusko Jaurlaritza/Gobierno Vasco.” Financial support from Gobierno Vasco (GIC07/92-IT-227-07) is also gratefully acknowledged. A. Duardo-Sánchez gratefully acknowledges Prof. Begoña Villaverde, Ph.D. and Prof. A. López-Díaz for financial support (project 2006/PX 207) of Department of Especial Public Law, Financial and Tributary Law Area, Faculty of Law from University of Santiago de Compostela (Spain), which was funded by Xunta de Galicia. This work is supported by the “Ibero-American Network of the Nano-Bio-Info-Cogno Convergent Technologies,” Ibero-NBIC Network (209RT0366) funded by CYTED (Ciencia y Tecnologa para el Desarrollo) and by the COMBIOMED Network, the grant (Ref. PIO52048 and RD07/0067/0005), funded by the Carlos III Health Institute.

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Authors and Affiliations

  1. Department of Information and Communication Technologies, Computer Science Faculty, University of A Coruña, 15071, A Coruña, Spain

    C. R. Munteanu, J. Dorado & Alejandro Pazos-Sierra

  2. Faculty of Pharmacy, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    F. Prado-Prado, L. G. Pérez-Montoto & S. Vilar

  3. Department of Microbiology and Parasitology, Faculty of Pharmacy, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    F. M. Ubeira

  4. Department of Inorganic Chemistry, Faculty of Pharmacy, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    A. Sanchez-Gonzaléz

  5. CEQA, Faculty of Chemistry and Pharmacy, UCLV, Santa Clara, 54830, Cuba

    M. Cruz-Monteagudo

  6. Department of Organic Chemistry II, Faculty of Science and Technology, University of the Basque Country/Euskal Herriko Unibertsitatea, Apto. 644, 48080, Bilbao, Spain

    S. Arrasate

  7. Department of Special Public Law, Faculty of Law, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    N. Sotomayor & E. Lete

  8. Joint Research Centre (JRC), EuropeanCommission, Institute for Health and Consumer Protection (IHPC), via E. Fermi, 2749–21027, Ispra, Varese, Italy

    A. Duardo-Sánchez & A. Díaz-López

  9. DuPont Haskell Global Centers for Health and Environmental Sciences, Newark, DE, 19711, USA

    G. Patlewicz

  10. Department of Microbiology and Parasitology, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    G. Patlewicz & H. González-Díaz

  11. Department of Organic Chemistry, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    H. González-Díaz

  12. Department of Inorganic Chemistry, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    H. González-Díaz & H. González-Díaz

Authors
  1. C. R. Munteanu
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  2. J. Dorado
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  3. Alejandro Pazos-Sierra
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  4. F. Prado-Prado
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  5. L. G. Pérez-Montoto
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  6. S. Vilar
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  7. F. M. Ubeira
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  8. A. Sanchez-Gonzaléz
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  9. M. Cruz-Monteagudo
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  10. S. Arrasate
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  11. N. Sotomayor
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  12. E. Lete
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  13. A. Duardo-Sánchez
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  14. A. Díaz-López
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  15. G. Patlewicz
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  16. H. González-Díaz
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Corresponding authors

Correspondence to C. R. Munteanu or H. González-Díaz .

Editor information

Editors and Affiliations

  1. Medizinische Informatik und Technik, Institute for Bioinformatics and Transla, UMIT-Private Universität für Gesundheits, Eduard Wallnöfer-Zentrum 1, Hall in Tirol, A-6060, Austria

    Matthias Dehmer

  2. Queen's University Belfast, School of Medicine, Dentistry, and Cell, Center for Cancer Research & Cell Biolog, Lisburn Road 97, Belfast, BT97BL, United Kingdom

    Frank Emmert-Streib

  3. Goethe-University Frankfurt am Main, Department of Philosophy and Historical, Center for Computing in the Humanities, Senckenberganlage 31, Frankfurt, 60325, Germany

    Alexander Mehler

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Munteanu, C.R. et al. (2011). Markov Entropy Centrality: Chemical, Biological, Crime, and Legislative Networks. In: Dehmer, M., Emmert-Streib, F., Mehler, A. (eds) Towards an Information Theory of Complex Networks. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4904-3_9

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