Abstract
Most of us recognize that connections are important. The science of connectivity has formalized and quantified this broad truism and produced a collection of concepts and tools that have proved to be remarkably useful in practice. With this brief opening chapter, we aim to prepare the reader for the cutting-edge and application-specific material to be found in the rest of the book by providing some motivation and background material. We also hope to give a taste of the excitement and the challenges that this area has to offer.
Network : Any thing reticulated or decussated, at equal distances, with interstices between the intersections.
Samuel Johnson
A Dictionary of the English Language, First Edition, 1755
Network : A large system consisting of many similar parts that are connected together to allow movement or communication between or along the parts or between the parts and a control centre.
Cambridge Advanced Learner’s Dictionary, on-line, 2010
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References
Albert, R., Barabási, A.L.: Topology of evolving networks: local events and universality. Phys. Rev. Lett. 85(24), 5234–5237 (2000)
Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)
Alon, U.: An Introduction to Systems Biology. Chapman & Hall/CRC Press, London (2006)
Amann, A., Pokrovskiy, A., Osborne, S., O’Brien, S.: Complex networks based on discrete-mode lasers. J. Phys. Conf. Ser. 138, 012001 (2008)
Badham, J., Stocker, R.: The impact of network clustering and assortativity on epidemic behaviour. Theor. Popul. Biol. 77(1), 71–75 (2010)
Barabási, A.L., Oltvai, Z.N.: Network biology: Understanding the cell’s functional organization. Nat. Rev. Genet. 5, 101–113 (2004)
Berg, J., Lassig, M., Wagner, A.: Structure and evolution of protein interaction networks: A statistical model for link dynamics and gene duplications. BMC Evol. Biol. 4, 51 (2004). arXiv:cond-mat/0207711
Bollobas, B.: Random Graphs. Academic Press, London (1985)
Caldarelli, G., Capocci, A., De Los Rios, P., Munõz, M.A.: Scale-free networks from varying vertex intrinsic fitness. Phys. Rev. Lett. 89, 258702 (2002)
Caldarelli, G.: Scale-Free Networks: Complex Webs in Nature and Technology. Oxford Finance Series. Oxford University Press, Oxford (2007)
Christakis, N.A., Fowler, J.H.: Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives. Little, Brown and Company, London (2009)
Conyon, M.J., Muldoon, M.R.: The small world of corporate boards. J. Bus. Finance Account. 33, 1321–1343 (2006)
Durrani, M.: Complexity made simple. Phys. World 23, 15 (2010). Special issue on complex affairs: Challenges in network science
Eagle, N., Pentland, A., Lazer, D.: Inferring social network structure using mobile phone data. Proc. Natl. Acad. Sci. USA 106, 15274–15278 (2009)
Erdős, P., Rényi, A.: On random graphs. Publ. Math. 6, 290–297 (1959)
Erdős, P., Rényi, A.: On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5, 17–61 (1960)
Erdős, P., Rényi, A.: On the strength of connectedness of a random graph. Acta Math. Acad. Sci. Hung. 12, 261–267 (1961)
Estrada, E.: Protein bipartivity and essentiality in the yeast protein–protein interaction network. J. Proteome Res. 5, 2177–2184 (2006)
Estrada, E., Hatano, N.: Statistical-mechanical approach to subgraph centrality in complex networks. Chem. Phys. Lett. 439, 247–251 (2007)
Estrada, E., RodrÃguez-Velázquez, J.A.: Subgraph centrality in complex networks. Phys. Rev. E 71, 056103 (2005)
Estrada, E., Higham, D.J., Hatano, N.: Communicability and multipartite structures in complex networks at negative absolute temperatures. Phys. Rev. E 77, 026102 (2008)
Estrada, E., Higham, D.J., Hatano, N.: Communicability betweenness in complex networks. Physica A 388, 764–774 (2009)
Estrada, E., Hatano, N.: Communicability in complex networks. Phys. Rev. E 77(3), 036111 (2008). doi:10.1103/PhysRevE.77.036111
Evlampiev, K., Isambert, H.: Modeling protein network evolution under genome duplication and domain shuffling. BMC Syst. Biol. 1, 49 (2007)
Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the internet topology. Comput. Commun. Rev. 29, 251–262 (1999)
Gautreau, A., Barrat, A., Barthelemy, M.: Microdynamics in stationary complex networks. Proc. Natl. Acad. Sci. USA 106, 8847–8852 (2009)
Gilbert, E.N.: Random graphs. Ann. Math. Stat. 30, 1141–1144 (1959)
Girvan, M., Newman, M.E.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA 99(12), 7821–7826 (2002)
Grindrod, P.: Range-dependent random graphs and their application to modeling large small-world proteome datasets. Phys. Rev. E 66, 066702 (2002)
Grindrod, P., Higham, D.J., Kalna, G.: Periodic reordering. IMA J. Numer. Anal. 30, 195–207 (2010)
Harary, F., Palmer, E.M.: Graph Theory and Theoretical Physics. Academic Press, New York (1968)
Higham, D.J., Rašajski, M., Pržulj, N.: Fitting a geometric graph to a protein–protein interaction network. Bioinformatics 24(8), 1093–1099 (2008)
Higham, D.J.: Unravelling small world networks. J. Comput. Appl. Math. 158, 61–74 (2003)
Holme, P., Liljeros, F., Edling, C.R., Kim, B.J.: Network bipartivity. Phys. Rev. E 68, 056107 (2003)
Itzkovitz, S., Milo, R., Kashtan, N., Ziv, G., Alon, U.: Subgraphs in random networks. Phys. Rev. E 68, 026127 (2003)
Jasny, B.R., Zahn, L., Marshall, E.: Connections. Science 325, 405 (2009). Special issue on complex systems and networks
Jeong, H., Mason, S.P., Barabási, A.L., Oltvai, Z.N.: Lethality and centrality in protein networks. Nature 411(6833), 41–42 (2001)
Kamper, L., Bozkurt, A., Rybacki, K., Geissler, A., Gerken, I., Stephan, K.E., Kötter, R.: An introduction to CoCoMac-Online. The online-interface of the primate connectivity database CoCoMac. In: Kötter, R. (ed.) Neuroscience Databases: A Practical Guide, pp. 155–169. Kluwer Academic, Norwell (2002)
Khanin, R., Wit, E.: How scale-free are gene networks? J. Comput. Biol. 13(3), 810–818 (2006)
Kleinberg, J.: Authoritative sources in a hyper-linked environment. In: Proceedings of the 9th ACM Conference on Hypertext and Hypermedia. ACM Press, New York (1998)
Kleinberg, J.M.: Navigation in a small world. Nature 406, 845 (2000)
Kleinfeld, J.S.: Could it be a big world after all? The ‘six degrees of separation’ myth. Society 39, 61–66 (2002)
Knuth, D.E.: The Art of Computer Programming, Volume 4, Fascicle 4: Generating All Trees—History of Combinatorial Generation. Addison-Wesley, Reading (2006)
Kuchaiev, O., Rasajski, M., Higham, D., Pržulj, N.: Geometric de-noising of protein–protein interaction networks. PLoS Comput. Biol. 5, 1000454 (2009)
Milenković, T., Pržulj, N.: Uncovering biological network function via graphlet degree signatures. Cancer Inform. 6, 257–273 (2008)
Milgram, S.: The small world problem. Psychol. Today 2, 60–67 (1967)
Milo, R., Shen-Orr, S.S., Itzkovitz, S., Kashtan, N., Chklovskii, D., Alon, U.: Network motifs: simple building blocks of complex networks. Science 298, 824–827 (2002)
Min, H.-K., Hwang, C.-S.: Comparison on the high school girls’ purchasing pattern of fashion products at online and offline markets. The Korean Society of Fashion Business 12, 124–137 (2008)
Moler, C.: The world’s largest matrix computation. MATLAB News and Notes (October 2002)
Morrison, J.L., Breitling, R., Higham, D.J., Gilbert, D.R.: A lock-and-key model for protein–protein interactions. Bioinformatics 2, 2012–2019 (2006)
Newman, J.: Leonhard Euler and the Königsberg bridges. Sci. Am. 189, 66–70 (1953)
Newman, M.E.: Scientific collaboration networks: I. network construction and fundamental results. Phys. Rev. E 64, 016131 (2001)
Newman, M.E.J.: Models of the small world: a review. J. Stat. Phys. 101, 819–841 (2000)
Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003)
Newman, M.E.J.: A measure of betweenness centrality based on random walks. Soc. Netw. 27, 39–54 (2005)
Newman, M.E.J., Moore, C., Watts, D.J.: Mean-field solution of the small-world network model. Phys. Rev. Lett. 84, 3201–3204 (2000)
Newman, M.: Assortative mixing in networks. Phys. Rev. Lett. 89, 208701 (2002)
Page, L., Brin, S., Motwani, R., Winograd, T.: The PageRank citation ranking: Bringing order to the web. Technical report, Stanford Digital Library Technologies Project (1998). http://www.citeseer.nj.nec.com/article/page98pagerank.html
Penrose, M.: Geometric Random Graphs. Oxford University Press, London (2003)
Pržulj, N., Higham, D.J.: Modelling protein–protein interaction networks via a stickiness index. J. R. Soc. Interface 3, 711–716 (2006)
Pržulj, N., Corneil, D.G., Jurisica, I.: Modeling interactome: Scale-free or geometric? Bioinformatics 20(18), 3508–3515 (2004)
Strogatz, S.H.: Exploring complex networks. Nature 410, 268–276 (2001)
Strogatz, S.H.: SYNC: The Emerging Science of Spontaneous Order. Hyperion, New York (2003)
Thomas, A., Cannings, R., Monk, N.A.M., Cannings, C.: On the structure of protein–protein interaction networks. Biochem. Soc. Trans. 31, 1491–1496 (2003)
Trinajstić, N.: Chemical Graph Theory. CRC Press, Boca Raton (1992)
Wagner, A.: How the global structure of protein interaction networks evolves. Proc. R. Soc. Lond. B, Biol. Sci. 270, 457–466 (2003)
Wasserman, S., Faust, K.: Social Network Analysis. Cambridge University Press, Cambridge (1994)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)
Ye, P., Peyser, B.D., Pan, X., Boeke, J.D., Spencer, F.A., Bader, J.S.: Gene function prediction from congruent synthetic lethal interactions in yeast. Mol. Syst. Biol. (2005). doi:10.1038/msb4100034
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Estrada, E., Fox, M., Higham, D.J., Oppo, GL. (2010). Complex Networks: An Invitation. In: Estrada, E., Fox, M., Higham, D., Oppo, GL. (eds) Network Science. Springer, London. https://doi.org/10.1007/978-1-84996-396-1_1
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