Community Structure: An Introduction
As a salient and important structural characteristic of real world networks, community structure is increasingly attracting much research attention from various fields. In this chapter, we will briefly introduce the research progress about the detection o
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Community Structure: An Introduction
1.1 Network Science: An Emerging Discipline Nature and society are composed of a wide variety of complex systems with very different scales. These systems range from cell to ecosystem, from the Internet to the Web, from power grid to various communication systems, from stock markets to other economic systems. Distinguishing from simple systems where the strength of interaction is uniquely determined by the physical distance, the components of complex systems highly interact with each other in the way unconstrained by certain distance measurements. These interactions influence and even determine the function and behavior of these complex systems. The whole system is not the simple aggregation of all these components. The system itself exhibits collective characteristics which are distinct from individual behavior. The collective behavior is emergent from spontaneous individual behaviors. We can see that disorder and order coexist in complex systems. To understand the function and behavior of complex systems, we need to study the pattern of interactions among components [1]. Network provides a powerful mathematical tool to represent and study complex systems [2]. For example, the scientific literature can be represented as a network of articles connected by citation relationships; the Web is a vast information network of Web pages linked by hyperlinks; the Internet is a network of routers or autonomous systems connected by various physical links or wireless links; society is a complex network where nodes are individuals and links correspond to various social relationships; the cell is depicted as networks of chemicals linked by chemical reactions; the stock market is best described as a network of traders linked by trading relationships. The underlying networks for these complex systems exhibit non-trivial topological characteristics. It requires considerable efforts to understand the structure of these complex networks and to provide some insights for understanding of the function of networks [3]. Network is absolutely not a new concept. Actually, the study of network has a long history and can date back to Euler’s solution of the puzzle of Köigsberg’s bridges in 1736 [4]. Since then, graph theory is gradually formed and has developed an arsenal of successful tools to study the properties of networks [5]. As the H.-W. Shen, Community Structure of Complex Networks, Springer Theses, DOI 10.1007/978-3-642-31821-4_1, © Springer-Verlag Berlin Heidelberg 2013
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Community Structure: An Introduction
most prominent development with respect to network in the last century, random networks, developed by Erd˝os and Rényi, place us in an ultimately random universe [6]. Meanwhile, scientists who do not believe in the wholly-random universe begin to investigate real world networks from various fields. Such kind of empirical studies gradually terminates the random universe for network and finally leads to the birth of a new discipline—network science [2, 3, 7–9]. The emergence of netwo
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