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Introduction

Complex networks

Recently, the vast number of observed non-trivial real-world networks, has triggered off a considerable interest in such systems (Barabasi & Albert, 2002; Dorogovtsev & Mendes, 2003; Bornholdt & Schuster (Eds.), 2003), and resulted in a number of interdisciplinary projects aiming at modelling, and understanding of networks. Moreover, since one has observed that many of these networks differ considerably from the traditional network models (i.e. periodic lattices, and pure random graphs), the notion of complex networks has emerged, which is a well-established concept nowadays. To be concrete, perhaps the most apparent property distinguishing such ‘complex’ real-world networks from the traditional models is their scale-free degree distribution P(k)~k-γ (Barabasi & Albert, 1999), which seems to be ubiquitous in nature. Further, many real-world networks exhibit small-world effect, and a high amount of clustering (Watts & Strogatz, 1998), and sometimes even a well-established fractal dimension (Song et al., 2005).

Why critical events in complex networks?

Every system entering into the critical region (in the sense of statistical physics) exhibits large scale fluctuations, and is very sensitive to presence of external fields (Kadanoff, 2000; Sornette, 2000), i.e. even very small instability may trigger off extreme events. It follows that stability / predictability of such a system changes dramatically, what may have important consequences for the whole system dynamics.

The noticed differences between traditional models, and complex networks allow us to expect large differences in critical behaviour of the latter with respect to former. Nowadays, due to the growing importance of networking (in particular, in social and technological systems), understanding of these differences constitutes one of the most important challenges in the new emerging science of complex networks.

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