AN INTRODUCTION TO THE PHYSICS OF COMPLEX NETWORKS

Geoff Rodgers

Brunel University

The aim of this lecture series is to give an introductory overview of the physics of complex networks. In particular the series will cover the growth and properties of complex networks, processes on complex networks, the connection between the theory of complex networks and random matrix theory and the applications of complex networks.
In Lecture I I will give an overview of the different classes of complex networks, the way in which they can be created and the different quantities that can be used to characterise their properties. In particular, basic models of scale free graphs and small world networks will be introduced and some of their properties identified.
In Lecture II I will examine diffusion, the dynamics of packet transport and the properties of spin systems, including their phase transitions, on complex networks.
In Lecture III the link between theories of complex networks and the properties of random matrices will be made. In addition, some of the major applications of complex networks will be introduced.
Review Articles:
[1] R. Albert, A.-L. Barabasi. Statistical mechanics of complex networks. Rev. Mod. Phys. 74 (2002) 47.
[2] S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes. Critical phenomena in complex networks. Rev. Mod. Phys. 80 (2008) 1275.
[3] D.J. Watts. Small Worlds. Princeton, 1999.
[4] J.F.F. Mendes et al. Science of Complex Networks. AIP, 2005.

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