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Examples include the internet and the worldwide web, metabolic networks, food webs, neural networks, communication and distribution networks, and social networks.
The study of networked systems has a history stretching back several centuries, but it has experienced a particular surge of interest in the last decade, especially in the mathematical sciences, partly as a result of the increasing availability of accurate large-scale data describing the topology of networks in the real world.
Many networks of interest in the sciences, including social networks, computer networks, and metabolic and regulatory networks, are found to divide naturally into communities or modules.
The problem of detecting and characterizing this community structure is one of the outstanding issues in the study of networked systems.
Let us approach this question in stages and focus initially on the problem of whether any good division of the network exists into just two communities.
Perhaps the most obvious way to tackle this problem is to look for divisions of the vertices into two groups so as to minimize the number of edges running between the groups.
Merely the finding that a network contains tightly knit groups at all can convey useful information: if a metabolic network were divided into such groups, for instance, it could provide evidence for a modular view of the network's dynamics, with different groups of nodes performing different functions with some degree of independence (11, 12).