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Table of Contents
Vol. 3, No. 1-3, 2006
Issue release date: August 2006
Section title: Network modelling
ComPlexUs 2006;3:131–146
(DOI:10.1159/000094195)

Spreading on Networks: A Topographic View

Canright G.S. · Engø-Monsen K.
Telenor R&D, Fornebu, Norway
email Corresponding Author

Abstract

We apply our previously developed method of ‘topographic’ analysis of networks to the problem of epidemic spreading. We consider the simplest form of epidemic spreading, namely the ‘SI’ model. We argue that the eigenvector centrality of a node is a good indicator of that node’s spreading power. From this we develop seven specific predictions. In particular, we predict that each region (as defined by our approach) will have its own S curve for cumulative adoption over time, and we describe the various phases of the S curve in terms of motion of the infection over the region. Our predictions are well supported by simulations. In particular, the significance of regions to epidemic spreading is clear. Finally, we develop a mathematical theory, giving partial support to our picture. The theory includes a precise quantitative definition of the spreading power of a node, and some approximate analytical results for epidemic spreading.

© 2006 S. Karger AG, Basel


  

Key Words

  • Epidemic spreading
  • Eigenvector centrality
  • Networks
  • Regions
  • Topography

References

  1. Canright G, Engø-Monsen K: Roles in networks. Sci Comput Program 2004; 53: 195–214.

    External Resources

  2. Newman MEJ: The structure and function of complex networks. SIAM Rev 2003; 45: 167–256.

    External Resources

  3. Pastor-Satorras R, Vespignani A: Epidemic spreading in scale-free networks. Phys Rev Lett 2001; 86: 3200–3203.
  4. Pastor-Satorras R, Vespignani A: Epidemic dynamics and endemic states in complex networks. Phys Rev E 2001; 63: 066117.
  5. Newman MEJ: Spread of epidemic disease on networks. Phys Rev E 2002; 66: 016128.
  6. Brauer F: A model for an SI disease in an age-structured population. Discrete Continuous Dyn Syst 2002;B2: 257–264.

    External Resources

  7. Wang Y, Chakrabarti D, Wang C, Faloutsos C: Epidemic spreading in real networks: an eigenvalue viewpoint. Proceedings of the 22nd Symposium on Reliable Distributed Systems (SRDS 2003), Florence, 2003, pp 25–34.
  8. Bonacich P: Factoring and weighting approaches to status scores and clique identification. J Math Soc 1972; 2: 113–120.
  9. Rogers EM: Diffusion of Innovations, ed 3. New York, Free Press, 1983.
  10. Jovanovic MA, Annexstein FS, Berman KA: Scalability issues in large peer-to-peer networks – a case study of Gnutella. Technical Report. University of Cincinnati, 2001.
  11. Canright G, Engø-Monsen K, Weltzien Å, Pourbayat F: Diffusion in social networks and disruptive innovations. Proceedings of IADIS e-Commerce 2004, Lisbon, 2004.
  12. Girvan M, Newman MEJ: Community structure in social and biological networks. Proc Natl Acad Sci USA 2002; 99: 8271–8276.

  

Author Contacts

Geoffrey S. Canright
Telenor R&D, B6d, Snarøyveien 30
NO–1331 Fornebu (Norway)
Tel. +47 91 81 5638, Fax +47 96 21 1086, E-Mail geoffrey.canright@telenor.com

  

Article Information

Published online: August 25, 2006
Number of Print Pages : 16
Number of Figures : 8, Number of Tables : 0, Number of References : 12

  

Publication Details

Complexus (Modelling in Systems Biology, Social, Cognitive and Information Sciences)

Vol. 3, No. 1-3, Year 2006 (Cover Date: August 2006)

Journal Editor: Atlan, H. (Paris/Jerusalem)
ISSN: 1424–8492 (print), 1424–8506 (Online)

For additional information: http://www.karger.com/CPU


Copyright / Drug Dosage / Disclaimer

Copyright: All rights reserved. No part of this publication may be translated into other languages, reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, microcopying, or by any information storage and retrieval system, without permission in writing from the publisher or, in the case of photocopying, direct payment of a specified fee to the Copyright Clearance Center.
Drug Dosage: The authors and the publisher have exerted every effort to ensure that drug selection and dosage set forth in this text are in accord with current recommendations and practice at the time of publication. However, in view of ongoing research, changes in goverment regulations, and the constant flow of information relating to drug therapy and drug reactions, the reader is urged to check the package insert for each drug for any changes in indications and dosage and for added warnings and precautions. This is particularly important when the recommended agent is a new and/or infrequently employed drug.
Disclaimer: The statements, opinions and data contained in this publication are solely those of the individual authors and contributors and not of the publishers and the editor(s). The appearance of advertisements or/and product references in the publication is not a warranty, endorsement, or approval of the products or services advertised or of their effectiveness, quality or safety. The publisher and the editor(s) disclaim responsibility for any injury to persons or property resulting from any ideas, methods, instructions or products referred to in the content or advertisements.

Abstract

We apply our previously developed method of ‘topographic’ analysis of networks to the problem of epidemic spreading. We consider the simplest form of epidemic spreading, namely the ‘SI’ model. We argue that the eigenvector centrality of a node is a good indicator of that node’s spreading power. From this we develop seven specific predictions. In particular, we predict that each region (as defined by our approach) will have its own S curve for cumulative adoption over time, and we describe the various phases of the S curve in terms of motion of the infection over the region. Our predictions are well supported by simulations. In particular, the significance of regions to epidemic spreading is clear. Finally, we develop a mathematical theory, giving partial support to our picture. The theory includes a precise quantitative definition of the spreading power of a node, and some approximate analytical results for epidemic spreading.

© 2006 S. Karger AG, Basel


  

Author Contacts

Geoffrey S. Canright
Telenor R&D, B6d, Snarøyveien 30
NO–1331 Fornebu (Norway)
Tel. +47 91 81 5638, Fax +47 96 21 1086, E-Mail geoffrey.canright@telenor.com

  

Article Information

Published online: August 25, 2006
Number of Print Pages : 16
Number of Figures : 8, Number of Tables : 0, Number of References : 12

  

Publication Details

Complexus (Modelling in Systems Biology, Social, Cognitive and Information Sciences)

Vol. 3, No. 1-3, Year 2006 (Cover Date: August 2006)

Journal Editor: Atlan, H. (Paris/Jerusalem)
ISSN: 1424–8492 (print), 1424–8506 (Online)

For additional information: http://www.karger.com/CPU


Article / Publication Details

First-Page Preview
Abstract of Network modelling

Published online: 9/1/2006
Issue release date: August 2006

Number of Print Pages: 16
Number of Figures: 8
Number of Tables: 0

ISSN: 1424-8492 (Print)
eISSN: 1424-8506 (Online)

For additional information: http://www.karger.com/CPU


Copyright / Drug Dosage

Copyright: All rights reserved. No part of this publication may be translated into other languages, reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, microcopying, or by any information storage and retrieval system, without permission in writing from the publisher or, in the case of photocopying, direct payment of a specified fee to the Copyright Clearance Center.
Drug Dosage: The authors and the publisher have exerted every effort to ensure that drug selection and dosage set forth in this text are in accord with current recommendations and practice at the time of publication. However, in view of ongoing research, changes in goverment regulations, and the constant flow of information relating to drug therapy and drug reactions, the reader is urged to check the package insert for each drug for any changes in indications and dosage and for added warnings and precautions. This is particularly important when the recommended agent is a new and/or infrequently employed drug.
Disclaimer: The statements, opinions and data contained in this publication are solely those of the individual authors and contributors and not of the publishers and the editor(s). The appearance of advertisements or/and product references in the publication is not a warranty, endorsement, or approval of the products or services advertised or of their effectiveness, quality or safety. The publisher and the editor(s) disclaim responsibility for any injury to persons or property resulting from any ideas, methods, instructions or products referred to in the content or advertisements.

References

  1. Canright G, Engø-Monsen K: Roles in networks. Sci Comput Program 2004; 53: 195–214.

    External Resources

  2. Newman MEJ: The structure and function of complex networks. SIAM Rev 2003; 45: 167–256.

    External Resources

  3. Pastor-Satorras R, Vespignani A: Epidemic spreading in scale-free networks. Phys Rev Lett 2001; 86: 3200–3203.
  4. Pastor-Satorras R, Vespignani A: Epidemic dynamics and endemic states in complex networks. Phys Rev E 2001; 63: 066117.
  5. Newman MEJ: Spread of epidemic disease on networks. Phys Rev E 2002; 66: 016128.
  6. Brauer F: A model for an SI disease in an age-structured population. Discrete Continuous Dyn Syst 2002;B2: 257–264.

    External Resources

  7. Wang Y, Chakrabarti D, Wang C, Faloutsos C: Epidemic spreading in real networks: an eigenvalue viewpoint. Proceedings of the 22nd Symposium on Reliable Distributed Systems (SRDS 2003), Florence, 2003, pp 25–34.
  8. Bonacich P: Factoring and weighting approaches to status scores and clique identification. J Math Soc 1972; 2: 113–120.
  9. Rogers EM: Diffusion of Innovations, ed 3. New York, Free Press, 1983.
  10. Jovanovic MA, Annexstein FS, Berman KA: Scalability issues in large peer-to-peer networks – a case study of Gnutella. Technical Report. University of Cincinnati, 2001.
  11. Canright G, Engø-Monsen K, Weltzien Å, Pourbayat F: Diffusion in social networks and disruptive innovations. Proceedings of IADIS e-Commerce 2004, Lisbon, 2004.
  12. Girvan M, Newman MEJ: Community structure in social and biological networks. Proc Natl Acad Sci USA 2002; 99: 8271–8276.