Abstract
The study of community networks has attracted considerable attention recently. In this paper, we propose an evolving community network model based on local events, the addition of new nodes intra-community and new links intra- or inter-community. Employing growth and preferential attachment mechanisms, we generate the network with a generalized power-law distribution of nodes’ degrees. Furthermore, we study epidemic spreading in the resulting network by the simple SIS model to understand the influence of the network structure on the dynamics. We find that the existence of communities in networks causes the critical behavior of the spreading dynamics and keeps epidemics endemic.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Erdös, P., Rényi, A.: On the Evolution of Random Graphs. Publ. Math. Inst. Hung. Acda. Sci. 5, 17–65 (1960)
Albert, R., Barabási, A.-L.: Statistical Mechanics of Complex Networks. Rev. Mod. Phys. 74, 47–97 (2002)
Watts, D.J., Strogatz, S.H.: Collective Dynamics of ‘‘Small-world’’Networks. Nature 393, 440–442 (1998)
Newman, M.E.J., Watts, D.J.: Scaling and Percolation in the Small-world Network Model. Phys. Rev. E 60, 7332–7342 (1999)
Barabási, A.-L., Albert, R.: Emergence of Scaling in Random Networks. Science 286, 509–512 (1999)
Krapivsky, P.L., Redner, S., Leyvraz, F.: Connectivity of Growing Random Networks. Phys. Rev. Lett. 85, 4629–4632 (2000)
Girvan, M., Newman, M.E.J.: Community Structure in Social and Biological Networks. Proc. Natl. Acad. Sci. USA 99, 7821–7826 (2002)
Bettencourt, L.M.A.: Tipping the Balances of a Small World. arXiv:cond-mat/0304321
Eriksen, K.A., Simonsen, I., Maslov, S., Sneppen, K.: Modularity and Extreme Edges of the Internet. Phys. Rev. Lett. 90, 148701 (2003)
Newman, M.E.J.: Fast Algorithm for Detecting Community Structure in Networks. Phys. Rev. E 69, 066133 (2004)
Duch, J., Arenas, A.: Community Detection in Complex Networks Using Extremal Optimization. Phys. Rev. E 72, 027104 (2005)
Watts, D.J., Dodds, P.S., Newman, M.E.J.: Identity and Search in Social Networks. Science 296, 1302–1305 (2002)
Grönlund, A., Holme, P.: Networking the Seceder Model: Group Formation in Social and Economic Systems. Phys. Rev. E 70, 036108 (2004)
Noh, J.D., Jeong, H.-C., Ahn, Y.-Y., Jeong, H.: Growing Network Model for Community with Group Structure. Phys. Rev. E 71, 036131 (2005)
Albert, R., Barabási, A.-L.: Topology of Evolving Networks: Local Events and Universality. Phys. Rev. Lett. 85, 5234 (2000)
Dorogovtsev, S.N., Mendes, J.F.F.: Scaling Behaviour of Developing and Decaying Networks. Europhys. Lett. 52, 33–39 (2000)
Li, X., Chen, G.: A Local-world Evolving Network Model. Physica A 328, 274–286 (2003)
Amaral, L.A.N., Scala, A., Barthelemy, M., Stanley, H.E.: Classes of Small-world Networks. Proc. Natl. Acad. Sci. USA 97, 11149–11152 (2000)
Zhang, P., Li, M., Wu, J., Di, Z., Fan, Y.: The analysis and Dissimilarity Comparison of Community Structure. Physica A 367, 577–585 (2006)
Biley, N.T.J.: The Mathematical Theory of Infectious Diseases and its Applications, 2nd edn. Griffin, London (1975)
Pastor-Satorras, R., Vespignani, A.: Epidemic Spreading in Scale-Free Networks. Phys. Rev. Lett. 86, 3200–3203 (2001)
Newman, M.E.J.: Spread of Epidemic Disease on Networks. Phys. Rev. E 66, 016128 (2002)
Warren, C.P., Sander, L.M., Sokolov, I.M.: Epidemics, Disorder, and Percolation. Physica A 325, 1–8 (2003)
Eguíluz, V.M., Klemm, K.: Epidemic Threshold in Structured Scale-free Networks. Phys. Rev. Lett. 89, 108701 (2002)
Barthélemy, M., Barrat, A., Pastor-Satorras, R., Vespignani, A.: Dynamical Patterns of Epidemic Outbreaks in Complex Heterogeneous Networks. J. Theor. Biol. 235, 275–288 (2005)
Vazquez, A.: Polynomial Growth in Branching Processes with Diverging Reproductive Number. Phys. Rev. Lett. 96, 038702 (2006)
Volz, E.: SIR Dynamics in Random Networks with Heterogeneous Connectivity. J. Math. Biol. 56, 293–310 (2008)
Pastor-Satorras, R., Vespignani, A.: Immunization of Complex Networks. Phys. Rev. E 65, 036104 (2002)
Cohen, R., Havlin, S., ben-Avraham, D.: Efficient Immunization Strategies for Computer Networks and Populations. Phys. Rev. Lett. 91, 247901 (2003)
Hufnagel, L., Brockmann, D., Geisel, T.: Forecast and Control of Epidemics in a Globalized World. Proc. Natl. Acad. Sci. USA 101, 15124–15129 (2004)
Gross, T., Dommar D’Lima, C.J., Blasius, B.: Epidemic Dynamics on an Adaptive Network. Phys. Rev. Lett. 96, 208701 (2006)
Kumpula, J.M., Onnela, J.-P., Saramäki, J., Kaski, K., Kertész, J.: Emergence of Communities in Weighted Networks. Phys. Rev. Lett. 99, 228701 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
About this paper
Cite this paper
Xu, XJ., Zhang, LJ., Yang, GH., Zhang, X. (2009). Impacts of Local Events on Communities and Diseases. In: Zhou, J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02466-5_33
Download citation
DOI: https://doi.org/10.1007/978-3-642-02466-5_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02465-8
Online ISBN: 978-3-642-02466-5
eBook Packages: Computer ScienceComputer Science (R0)