Complex Network Modeling: A New Approach to Neurosciences
Recently, many seemingly diverse systems have been found to share unique structural properties that in their turn greatly influence the dynamical features and function of these systems. In this chapter, we focus on recent discoveries about the structure and function of complex networks to show how emergent properties in neuronal systems can be studied using the tools developed in the last several years. We first introduce basic notions to understand what a complex network is and how one can characterize its topology. Next, we discuss some topological properties recently revealed in the literature and their connections to the structural properties of other complex networks found in many fields of science. The second part of this chapter is devoted to revise the relationship between the structural properties of brain-like systems and their dynamical behavior. In particular, we pay attention to synchronization phenomena, quite relevant in many contexts of neurosciences. We round off the chapter by outlining some perspectives and discussing future and promising lines of research.
KeywordsDegree Distribution Cluster Coefficient Brain Network Real World Network Detailed Balance Condition
I am grateful to my collaborators on the subjects discussed here and would also like to thank A. Arenas, S. Boccaletti, A. Díaz-Guilera, L. M. Floria, J. Gómez-Gardeñes, and V. Latora for many helpful discussions on the structure and dynamics of complex networks during the last several years. The author is supported by MEC through the Ramón y Cajal Program. This work has been partially supported by the Spanish DGICYT Projects FIS2006-12781-C02-01 and FIS2005-00337 and by the European NEST Pathfinder project GABA under contract 043309.
- J. A. Acebron, L. L. Bonilla, C. J. Perez Vicente, F. Ritort, and R. Spigler. The Kuramoto model: A simple paradigm for synchronization phenomena. Rev. Mod. Phys. 77, 137–185 (2005).Google Scholar
- R. D. Alba. A graph-theoretic definition of a sociometric clique. J. Math. Social. 3, 113 (1973).Google Scholar
- L. Danon, A. Diaz-Guilera, J. Duch, and A. Arenas. Comparing community structure identification. J. Stat. Mech. P09008 (2005).Google Scholar
- V. Latora and M. Marchiori. Economic Small-World Behavior in Weighted Networks. Eur. Phys. J. B32, 249 (2003).Google Scholar
- V. Latora and M. Marchiori. A measure of centrality based on the network efficiency. Preprint cond-mat/0402050.Google Scholar
- M. Marchiori and V. Latora. Harmony in the small-world. Physica A285, 539 (2000).Google Scholar
- M. E. J. Newman. Mixing patterns in networks. Phys. Rev. E67, 026126 (2003a).Google Scholar
- J. Scott, Social Network Analysis: A Handbook (Sage Publications, London, 2nd ed., 2000).Google Scholar
- S. Wasserman and K. Faust, Social Networks Analysis (Cambridge University Press, Cambridge, 1994).Google Scholar
- D. J. Watts, Small Worlds: The Dynamics of Networks Between Order and Randomness (Princeton University Press, Princeton, NJ, 1999).Google Scholar