The tremendous progress in the natural sciences we witnessed in the last century was based on the reductionist approach, allowing us to predict the behavior of a system from the understanding of its (often identical) elementary constituents and their individual interactions. However, our ability to understand simple fundamental laws governing individual "building blocks" is a far cry from being able to predict the overall behavior of a complex system.5 Additionally, the building blocks of most complex systems, and hence the nature of their interactions, vary dramatically, rendering the traditional approaches obsolete. During the last few years, network approaches have shown great promise as a new tool to analyze and understand complex systems.1'9,17,61 For example, technological information systems like the internet and the world-wide web are naturally modeled as networks, where the nodes are routers23,63 or web-pages2,10,47 and the links are physical wires or URL's respectively. The analysis of societies also lends itself naturally to a network description, with people as nodes and the connections between the nodes as friendships,50 collaborations,44'65 sexual contacts48 or coauthorship of scientific papers52'57a to name a few possibilities. It seems that the closer we look at the world surrounding us, the more we realize that we are hopelessly entangled in myriads of interacting webs, and to describe them we need to understand the architecture of the various networks nature and technology offers us.

In biology, networks appear in many disparate systems, ranging from food webs in ecology to biochemical interactions in molecular biology. In particular in the cell the variety of interactions between genes, proteins and metabolites are well captured by networks. During

"Corresponding author: Albert-László Barabási—Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, U.S.A. Email: [email protected]

Power Laws, Scale-Free Networks and Genome Biology, edited by Eugene V. Koonin, Yuri I. Wolf and Georgy P. Karev. ©2006 and Springer Science+Business Media.

Figure 1. Characterizing degree distributions. For the power-law degree distribution (A), there exists no typical node, while for single peaked distributions (B), most nodes are well represented by the average (typical) node with degree (k ).

the last decade, genomics has unleashed a downright flood of molecular interaction data. The nascent field of transcriptomics and proteomics have followed suit with analysis of protein levels under various conditions and genome wide analysis of gene expression at the mRNA level.11'12,53 Thus, protein-protein interaction maps have been generated for a variety of organisms including viruses,25 prokaryotes like H. pylori54 and eukaryotes like S. cimwi^7'35'39,40'42'58'62 and C. elegans.64 In this chapter we will discuss recent results and developments in the study and characterization of naturally occurring networks, with focus on cellular ones.

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