Abstract
A complex network is a structure made up of nodes connected by one or more specific types of interdependency. Nodes represent individuals, groups, or organizations, while connections (links, edges or ties) represent relations such as friendship, economic deals, internet connections, neuron connections, protein interactions, etc. The resulting graph-based structures are often very complex, being social networks the most popular application, but the analysis of these structures has carried out a great number of research papers in fields like: Economics, Telecommunications, Biology, Artificial Intelligence, Bioinformatics, Anthropology, Information Science, Social Psychology, Sociolinguistics, among others. Network Theory has emerged as a key technique to be applied in order to model, analyze, simulate and understand those complex network topologies; from a static and a dynamic point of view.
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
Notes
- 1.
In this book we use the Cartesian distance to determinate how far is a node from another in a spatial network. However, the Manhattan distance is also popular in square lattices, and counts the number of horizontal and vertical segments between two nodes.
- 2.
The small-world phenomenon is popularly known in as the six degrees of separation, which is based on the idea that the average diameter of a whole social network is shorter than six.
References
Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)
Chen, F., Chen, Z., Wang, X., Yuan, Z.: The average path length of scale free networks. Commun. Nonlinear Sci. Numer. Simul. 13(7), 1405–1410 (2008)
Cohen, R., Havlin, S.: Scale-free networks are ultrasmall. Phys. Rev. Lett. 90(5), 058701 (2003)
Cohen, R., Havlin, S.: Complex Networks: Structure, Stability and Function. Cambridge University Press, Cambridge (2010)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)
Erdös, P., Rényi, A.: On random graphs. Publ. Math. 6, 290–297 (1959)
Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the Internet topology. Comput. Commun. Rev. 29, 251 (1999)
Newman, M.E.J.: Networks: An Introduction. Oxford University Press, Oxford (2010)
Shields, R.: Cultural topology: the seven bridges of Konigsburg, 1736. Theory Cult. Soc. 29(4–5), 43–57 (2012)
Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393(6684), 440–442 (1998)
Watts, D.J.: Six Degrees: The Science of a Connected Age. Norton, New York (2003)
Wikimedia Commons by Arpad Horvath - Own work, CC BY-SA 3.0. https://commons.wikimedia.org/wiki/File:Barabasi-albert_model_degree_distribution.svg
Wikimedia Commons by Claudio Rocchini - Own work, CC BY-SA 2.5. https://commons.wikimedia.org/wiki/File:Graph_betweenness.svg
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Burguillo, J.C. (2018). Complex Networks. In: Self-organizing Coalitions for Managing Complexity. Emergence, Complexity and Computation, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-319-69898-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-69898-4_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-69896-0
Online ISBN: 978-3-319-69898-4
eBook Packages: EngineeringEngineering (R0)