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Topology and Dynamics of Complex Networks FRES1010 Complex Adaptive Systems Eileen Kraemer Fall 2005.

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Presentation on theme: "Topology and Dynamics of Complex Networks FRES1010 Complex Adaptive Systems Eileen Kraemer Fall 2005."— Presentation transcript:

1 Topology and Dynamics of Complex Networks FRES1010 Complex Adaptive Systems Eileen Kraemer Fall 2005

2 Based on … Strogatz (2001), Barabási & Bonabeau (2003), Wang, X. F. (2002)

3 Topology and Dynamics of Complex Networks Introduction Three structural metrics Four structural models Structural case studies Node dynamics and self-organization Bibliography

4 Introduction Examples of complex networks Elementary features Motivations

5 Examples of complex networks: geometric, regular

6 Examples of complex networks: semi-geometric, irregular

7 Elementary features: node diversity and dynamics

8 Elementary features: edge diversity and dynamics

9 Elementary features: Network Evolution

10 Motivations complex networks are the backbone of complex systems every complex system is a network of interaction among numerous smaller elements some networks are geometric or regular in 2-D or 3-D space other contain long-range connections or are not spatial at all understanding a complex system = break down into parts + reassemble network anatomy is important to characterize because structure affects function (and vice-versa) ex: structure of social networks prevent spread of diseases control spread of information (marketing, fads, rumors, etc.) ex: structure of power grid / Internet understand robustness and stability of power / data transmission

11 Three structural metrics Average path length Degree distribution(connectivity) Clustering coefficient

12 Structural metrics: Average path length

13 Structural Metrics: Degree distribution(connectivity)

14 Structural Metrics: Clustering coefficient

15 Four structural models Regular networks Random networks Small-world networks Scale-free networks

16 Regular networks – fully connected

17 Regular networks – Lattice

18 Regular networks – Lattice: ring world

19 Random networks

20 Random Networks

21 Small-world networks

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25 Scale-free networks

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31 Case studies Internet World Wide Web Actors & scientists Neural networks Cellular metabolism

32 The Internet

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35 The World Wide Web

36 World Wide Web

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38 Actors

39 Mathematicians & Computer Scientists

40 Node dynamics and self- organization Node dynamics Attractors in full & lattice networks Synchronization in full networks Waves in lattice networks Epidemics in complex networks

41 Node dynamics: individual node

42 Node dynamics: coupled nodes

43 Node dynamics and self-organization

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48 Node dynamics and self-organization: Epidemics in complex networks

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50 Bibliography Reviews Barabási, A.-L. (2002) Linked: The New Science of Networks.Perseus Books. Barabási, A.-L. and Bonabeau, E. (2003) Scale- free networks. Scientific American, 288: Scale- free networks Strogatz, S. H. (2001) Exploring complex networks. Nature, 410(6825): Exploring complex networks Wang, X. F. (2002) Complex networks: topology, dynamics and synchronization. International Journal of Bifurcation and Chaos, 12(5):

51 Bibliography Studies Albert, R., Jeong, H. & Barabási, A.-L. (1999) Diameter of the World Wide Web. Nature401: Albert, R., Jeong, H. & Barabási, A.-L. (2000) Attack and error tolerance in complex networks. Nature406: Barabási, A.-L. and Albert, R. (1999) Emergence of scaling in random networks. Science, 286(5439): Erdős, P. & Rényi, A. (1960) On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci.5: Faloutsos, M., Faloutsos, P. & Faloutsos, C. (1999) On power-law relationships of the Internet topology. Comput. Commun. Rev.29: Pastor-Satorras, R. & Vespignani, A. (2001) Epidemic dynamics and endemic states in complex networks. Phys. Rev.E63(066117): 1-8. Watts, D. J. and Strogatz, S. H. (1998) Collective dynamics of "small- world" networks. Nature, 393(6684):


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