1 - Introduction
Published online by Cambridge University Press: 01 March 2011
Summary
Despite the fact that complex networks are the driving force behind the investigation of the spectra of graphs, it is not the purpose of this book to dwell on complex networks. A generally accepted, all-encompassing definition of a complex network does not seem to be available. Instead, complex networks are understood by instantiation: the Internet, transportation (car, train, airplane) and infrastructural (electricity, gas, water, sewer) networks, biological molecules, the human brain network, social networks, software dependency networks, are examples of complex networks. By now, there is such a large literature about complex networks, predominantly in the physics community, that providing a detailed survey is a daunting task. We content ourselves here with referring to some review articles by Strogatz (2001); Newman et al. (2001); Albert and Barabasi (2002); Newman (2003b), and to books in the field by Watts (1999); Barabasi (2002); Dorogovtsev and Mendes (2003); Barrat et al. (2008); Dehmer and Emmert-Streib (2009); Newman (2010), and to references in these works. Application of spectral graph theory to chemistry and physics are found in Cvetković et al. (1995, Chapter 8).
Complex networks can be represented by a graph, denoted by G, consisting of a set N of N nodes connected by a set ℒ of L links. Sometimes, nodes and links are called vertices and edges, respectively, and are correspondingly denoted by the set V and E.
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- Graph Spectra for Complex Networks , pp. 1 - 10Publisher: Cambridge University PressPrint publication year: 2010
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