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2012 | OriginalPaper | Buchkapitel

6. Structural Decompositions of Complex Networks

verfasst von : Rong Yang, Leyla Zhuhadar, Olfa Nasraoui

Erschienen in: Computational Social Networks

Verlag: Springer London

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Abstract

In complex network research, a number of different ways of studying the macroscopic structure of a network have been developed. This chapter provides an overview of the most important ones. The primary example is thebow-tie decomposition. We provide a precise formal definition for the decomposition as well as an algorithm for computing it. The closely related Daisy model and a fractal approach are also discussed in some detail. Some other approaches are discussed briefly.

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Literatur
1.
Zurück zum Zitat Adamic, L., Adar, E.: How to search a social network. Soc. Netw. 27(3), 187–203 (2005)CrossRef Adamic, L., Adar, E.: How to search a social network. Soc. Netw. 27(3), 187–203 (2005)CrossRef
2.
Zurück zum Zitat Ahuja, G.: Collaboration networks, structural holes, and innovation: a longitudinal study. Adm. Sci. Q. 45(3), 425–455 (2000)MathSciNetCrossRef Ahuja, G.: Collaboration networks, structural holes, and innovation: a longitudinal study. Adm. Sci. Q. 45(3), 425–455 (2000)MathSciNetCrossRef
3.
Zurück zum Zitat Albert, R.: Jeong, H., Barabási, A.L.: The diameter of the world wide web. Arxiv preprint cond-mat/9907038 (1999) Albert, R.: Jeong, H., Barabási, A.L.: The diameter of the world wide web. Arxiv preprint cond-mat/9907038 (1999)
4.
Zurück zum Zitat Albert, R., Albert, I., Nakarado, G.L.: Structural vulnerability of the North American power grid. Phys. Rev. E. 69(2), 25103 (2004)CrossRef Albert, R., Albert, I., Nakarado, G.L.: Structural vulnerability of the North American power grid. Phys. Rev. E. 69(2), 25103 (2004)CrossRef
5.
Zurück zum Zitat Arasu, A., Novak, J., Tomkins, A., Tomlin, J.: PageRank computation and the structure of the web: experiments and algorithms. In: Proceedings of the Eleventh International World Wide Web Conference, Poster Track, pp. 107–117. Citeseer, Honolulu (2002) Arasu, A., Novak, J., Tomkins, A., Tomlin, J.: PageRank computation and the structure of the web: experiments and algorithms. In: Proceedings of the Eleventh International World Wide Web Conference, Poster Track, pp. 107–117. Citeseer, Honolulu (2002)
6.
Zurück zum Zitat Arquilla, J., Ronfeldt, D., Zanini, M., Naval Postgraduate School Monterey CA Graduate School of Operational, and Information Sciences: Networks, Netwar, and Information-Age Terrorism. Defense Technical Information Center, Fort Belvoir (1999) Arquilla, J., Ronfeldt, D., Zanini, M., Naval Postgraduate School Monterey CA Graduate School of Operational, and Information Sciences: Networks, Netwar, and Information-Age Terrorism. Defense Technical Information Center, Fort Belvoir (1999)
7.
Zurück zum Zitat Baldi, P., Frasconi, P., Smyth, P.: Modeling the Internet and the Web: Probabilistic Methods and Algorithms. Wiley, Chichester/Hoboken (2003) Baldi, P., Frasconi, P., Smyth, P.: Modeling the Internet and the Web: Probabilistic Methods and Algorithms. Wiley, Chichester/Hoboken (2003)
9.
Zurück zum Zitat Barabasi, A.L., Jeong, H., Néda, Z., Ravasz, E., Schubert, A., Vicsek, T.: Evolution of the social network of scientific collaborations. Phys. A Stat. Mech. Appl. 311(3–4), 590–614 (2002)MATHCrossRef Barabasi, A.L., Jeong, H., Néda, Z., Ravasz, E., Schubert, A., Vicsek, T.: Evolution of the social network of scientific collaborations. Phys. A Stat. Mech. Appl. 311(3–4), 590–614 (2002)MATHCrossRef
10.
Zurück zum Zitat Barla, P., Constantatos, C.: Airline network structure under demand uncertainty. Transp. Res. E Logist. Transp. Rev. 36(3), 173–180 (2000)CrossRef Barla, P., Constantatos, C.: Airline network structure under demand uncertainty. Transp. Res. E Logist. Transp. Rev. 36(3), 173–180 (2000)CrossRef
11.
Zurück zum Zitat Batagelj, V., Mrvar, A.: Pajek-program for large network analysis. Connections 21(2), 47–57 (1998) Batagelj, V., Mrvar, A.: Pajek-program for large network analysis. Connections 21(2), 47–57 (1998)
12.
Zurück zum Zitat Batagelj, V., Mrvar, A.: Pajek analysis and visualization of large networks. In: Mutzel, P., Jünger, M., Leipert, S. (eds.) Graph Drawing, pp. 8–11. Springer, Berlin (2002) Batagelj, V., Mrvar, A.: Pajek analysis and visualization of large networks. In: Mutzel, P., Jünger, M., Leipert, S. (eds.) Graph Drawing, pp. 8–11. Springer, Berlin (2002)
13.
Zurück zum Zitat Bjorneborn, L., Danmarks biblioteksskole: Small-World Link Structures Across an Academic Web Space: a Library and Information Science Approach. Department of Information Studies, Royal School of Library and Information Science, Copenhagen (2004) Bjorneborn, L., Danmarks biblioteksskole: Small-World Link Structures Across an Academic Web Space: a Library and Information Science Approach. Department of Information Studies, Royal School of Library and Information Science, Copenhagen (2004)
14.
Zurück zum Zitat Bjorneborn, L.: ‘Mini small worlds’ of shortest link paths crossing domain boundaries in an academic Web space. Scientometrics 68(3), 395–414 (2006)CrossRef Bjorneborn, L.: ‘Mini small worlds’ of shortest link paths crossing domain boundaries in an academic Web space. Scientometrics 68(3), 395–414 (2006)CrossRef
15.
Zurück zum Zitat Boyd, D.M., Ellison, N.B.: Social network sites: definition, history, and scholarship. J Comput. Mediat. Commun. 13(1), 210–230 (2008)CrossRef Boyd, D.M., Ellison, N.B.: Social network sites: definition, history, and scholarship. J Comput. Mediat. Commun. 13(1), 210–230 (2008)CrossRef
16.
Zurück zum Zitat Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A., Wiener, J.: Graph structure in the web. Comput. Netw. 33(1–6), 309–320 (2000)CrossRef Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A., Wiener, J.: Graph structure in the web. Comput. Netw. 33(1–6), 309–320 (2000)CrossRef
17.
Zurück zum Zitat Caldarelli, G., Marchetti, R., Pietronero, L.: The fractal properties of internet. EPL (Europhys. Lett.) 52, 386 (2000) Caldarelli, G., Marchetti, R., Pietronero, L.: The fractal properties of internet. EPL (Europhys. Lett.) 52, 386 (2000)
18.
Zurück zum Zitat Chassin, D.P., Posse, C.: Evaluating North American electric grid reliability using the Barabasi-albert network model. Phys. A Stat. Mech. Appl. 355(2–4), 667–677 (2005)CrossRef Chassin, D.P., Posse, C.: Evaluating North American electric grid reliability using the Barabasi-albert network model. Phys. A Stat. Mech. Appl. 355(2–4), 667–677 (2005)CrossRef
19.
20.
Zurück zum Zitat Dill, S., Kumar, R., McCurley, K.S., Rajagopalan, S., Sivakumar, D., Tomkins, A.: Self-similarity in the web. ACM Trans. Internet Technol. (TOIT) 2(3), 205–223 (2002) Dill, S., Kumar, R., McCurley, K.S., Rajagopalan, S., Sivakumar, D., Tomkins, A.: Self-similarity in the web. ACM Trans. Internet Technol. (TOIT) 2(3), 205–223 (2002)
21.
Zurück zum Zitat Dombroski, M., Carley, K.M.: NETEST: estimating a terrorist networks structure. In: CASOS Conference Proceedings, Pittsburgh, p. 2 (2002) Dombroski, M., Carley, K.M.: NETEST: estimating a terrorist networks structure. In: CASOS Conference Proceedings, Pittsburgh, p. 2 (2002)
22.
Zurück zum Zitat Donato, D., Leonardi, S., Millozzi, S., Tsaparas, P.: Mining the inner structure of the web graph. J. Phys. A Math. Theor. 41, 224017 (2008)MathSciNetCrossRef Donato, D., Leonardi, S., Millozzi, S., Tsaparas, P.: Mining the inner structure of the web graph. J. Phys. A Math. Theor. 41, 224017 (2008)MathSciNetCrossRef
23.
Zurück zum Zitat Dunne, J.A.: The network structure of food webs. Ecol. Netw. Link. Struct. Dyn. Food Webs. pp. 27–86 (2006) Dunne, J.A.: The network structure of food webs. Ecol. Netw. Link. Struct. Dyn. Food Webs. pp. 27–86 (2006)
24.
Zurück zum Zitat Dunne, J.A., Williams, R.J., Martinez, N.D.: Network structure and robustness of marine food webs. Mar. Ecol. Prog. Ser. 273, 291–302 (2004)CrossRef Dunne, J.A., Williams, R.J., Martinez, N.D.: Network structure and robustness of marine food webs. Mar. Ecol. Prog. Ser. 273, 291–302 (2004)CrossRef
25.
Zurück zum Zitat Easley, D., Kleinberg, J.: Networks, Crowds, and Markets: Reasoning About a Highly Connected World. Cambridge University Press, New York (2010)MATHCrossRef Easley, D., Kleinberg, J.: Networks, Crowds, and Markets: Reasoning About a Highly Connected World. Cambridge University Press, New York (2010)MATHCrossRef
26.
Zurück zum Zitat Erdos, P., Renyi, A.: On random graphs I. Publ. Math. Debr. 6(290–297), 156 (1959)MathSciNet Erdos, P., Renyi, A.: On random graphs I. Publ. Math. Debr. 6(290–297), 156 (1959)MathSciNet
27.
Zurück zum Zitat Erdos, P., Rényi, A.: On the Evolution of Random Graphs. Citeseer (1960) Erdos, P., Rényi, A.: On the Evolution of Random Graphs. Citeseer (1960)
28.
Zurück zum Zitat Gastner, M.T., Newman, M.E.J.: The spatial structure of networks. Eur. Phys. J. B-Condens. Matter Complex Syst. 49(2), 247–252 (2006)CrossRef Gastner, M.T., Newman, M.E.J.: The spatial structure of networks. Eur. Phys. J. B-Condens. Matter Complex Syst. 49(2), 247–252 (2006)CrossRef
29.
Zurück zum Zitat Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA 99(12), 7821 (2002)MathSciNetMATHCrossRef Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA 99(12), 7821 (2002)MathSciNetMATHCrossRef
30.
Zurück zum Zitat Gross, T., DLima, C.J.D., Blasius, B.: Epidemic dynamics on an adaptive network. Phys. Rev. Lett. 96(20), 208701 (2006) Gross, T., DLima, C.J.D., Blasius, B.: Epidemic dynamics on an adaptive network. Phys. Rev. Lett. 96(20), 208701 (2006)
31.
Zurück zum Zitat Hirate, Y., Kato, S., Yamana, H.: Web structure in 2005. Algorithms Models Web-Graph 36–46 (2008) Hirate, Y., Kato, S., Yamana, H.: Web structure in 2005. Algorithms Models Web-Graph 36–46 (2008)
32.
Zurück zum Zitat Kinney, R., Crucitti, P., Albert, R., Latora, V.: Modeling cascading failures in the North American power grid. Eur. Phys. J. B-Condens. Matter Complex Syst. 46(1), 101–107 (2005)CrossRef Kinney, R., Crucitti, P., Albert, R., Latora, V.: Modeling cascading failures in the North American power grid. Eur. Phys. J. B-Condens. Matter Complex Syst. 46(1), 101–107 (2005)CrossRef
33.
Zurück zum Zitat Krebs, V.E.: Mapping networks of terrorist cells. Connections 24(3), 43–52 (2002) Krebs, V.E.: Mapping networks of terrorist cells. Connections 24(3), 43–52 (2002)
34.
Zurück zum Zitat Kumar, R., Raghavan, P., Rajagopalan, S., Sivakumar, D., Tomkins, A., Upfal, E.: Stochastic models for the web graph. In: Foundations of Computer Science, 2000. Proceedings. 41st Annual Symposium on, pp. 57–65. IEEE, Los Alamitos (2002) Kumar, R., Raghavan, P., Rajagopalan, S., Sivakumar, D., Tomkins, A., Upfal, E.: Stochastic models for the web graph. In: Foundations of Computer Science, 2000. Proceedings. 41st Annual Symposium on, pp. 57–65. IEEE, Los Alamitos (2002)
35.
Zurück zum Zitat Kumar, R., Raghavan, P., Rajagopalan, S., Tomkins, A.: The web and social networks. IEEE Comput. 35(11), 32–36 (2002)CrossRef Kumar, R., Raghavan, P., Rajagopalan, S., Tomkins, A.: The web and social networks. IEEE Comput. 35(11), 32–36 (2002)CrossRef
36.
Zurück zum Zitat May, R.M.: Network structure and the biology of populations. Trends Ecol. Evol. 21(7), 394–399 (2006)CrossRef May, R.M.: Network structure and the biology of populations. Trends Ecol. Evol. 21(7), 394–399 (2006)CrossRef
37.
Zurück zum Zitat May, R.M., Lloyd, A.L.: Infection dynamics on scale-free networks. Phys. Rev. E 64(6), 66112 (2001)CrossRef May, R.M., Lloyd, A.L.: Infection dynamics on scale-free networks. Phys. Rev. E 64(6), 66112 (2001)CrossRef
38.
Zurück zum Zitat Meyers, L.A., Pourbohloul, B., Newman, M.E.J., Skowronski, D.M., Brunham, R.C.: Network theory and SARS: predicting outbreak diversity. J. Theor. Biol. 232(1), 71–81 (2005)MathSciNetCrossRef Meyers, L.A., Pourbohloul, B., Newman, M.E.J., Skowronski, D.M., Brunham, R.C.: Network theory and SARS: predicting outbreak diversity. J. Theor. Biol. 232(1), 71–81 (2005)MathSciNetCrossRef
39.
Zurück zum Zitat Newman, M.E.J.: Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. Phys. Rev. E 64(1), 16132 (2001) Newman, M.E.J.: Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. Phys. Rev. E 64(1), 16132 (2001)
41.
Zurück zum Zitat Newman, M.E.J.: Spread of epidemic disease on networks. Phys. Rev. E 66(1), 16128 (2002)CrossRef Newman, M.E.J.: Spread of epidemic disease on networks. Phys. Rev. E 66(1), 16128 (2002)CrossRef
42.
Zurück zum Zitat Newman, M.E.J.: The structure and function of complex networks. Arxiv preprint cond-mat/0303516 (2003) Newman, M.E.J.: The structure and function of complex networks. Arxiv preprint cond-mat/0303516 (2003)
43.
Zurück zum Zitat Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69(2), 26113 (2004)CrossRef Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69(2), 26113 (2004)CrossRef
44.
Zurück zum Zitat Newman, M.E.J., Forrest, S., Balthrop, J.: Email networks and the spread of computer viruses. Phys. Rev. E. 66(3), 35101 (2002)CrossRef Newman, M.E.J., Forrest, S., Balthrop, J.: Email networks and the spread of computer viruses. Phys. Rev. E. 66(3), 35101 (2002)CrossRef
45.
Zurück zum Zitat Nooy, W., Mrvar, A., Batagelj, V.: Exploratory social network analysis with Pajek. Cambridge University Press, New York (2005)CrossRef Nooy, W., Mrvar, A., Batagelj, V.: Exploratory social network analysis with Pajek. Cambridge University Press, New York (2005)CrossRef
46.
Zurück zum Zitat Porter, M.A., Onnela, J.P., Mucha, P.J.: Communities in networks. Not. Am. Math. Soc. 56(9), 1082–1097 (2009)MathSciNetMATH Porter, M.A., Onnela, J.P., Mucha, P.J.: Communities in networks. Not. Am. Math. Soc. 56(9), 1082–1097 (2009)MathSciNetMATH
47.
Zurück zum Zitat Ressler, S.: Social network analysis as an approach to combat terrorism: past, present, and future research. Homel. Secur. Aff. 2(2), 1–10 (2006) Ressler, S.: Social network analysis as an approach to combat terrorism: past, present, and future research. Homel. Secur. Aff. 2(2), 1–10 (2006)
48.
Zurück zum Zitat Rothenberg, R.: From whole cloth: making up the terrorist network. (2001), New York Times Rothenberg, R.: From whole cloth: making up the terrorist network. (2001), New York Times
49.
Zurück zum Zitat Siganos, G., Tauro, S.L., Faloutsos, M.: Jellyfish: a conceptual model for the as internet topology. J. Commun. Netw. 8(3), 339 (2006) Siganos, G., Tauro, S.L., Faloutsos, M.: Jellyfish: a conceptual model for the as internet topology. J. Commun. Netw. 8(3), 339 (2006)
50.
Zurück zum Zitat Song, C., Havlin, S., Makse, H.A.: Self-similarity of complex networks. Nature 433(7024), 392–395 (2005) Song, C., Havlin, S., Makse, H.A.: Self-similarity of complex networks. Nature 433(7024), 392–395 (2005)
51.
Zurück zum Zitat Tanaka, R., Csete, M., Doyle, J.: Highly optimised global organisation of metabolic networks. IEE Proc. Syst. Biol. 152(4), 179–184 (2005) Tanaka, R., Csete, M., Doyle, J.: Highly optimised global organisation of metabolic networks. IEE Proc. Syst. Biol. 152(4), 179–184 (2005)
52.
Zurück zum Zitat Tu, Y.: How robust is the internet. Nature 406(6794), 353–354 (2000)CrossRef Tu, Y.: How robust is the internet. Nature 406(6794), 353–354 (2000)CrossRef
53.
Zurück zum Zitat Vazquez, A., Pastor-Satorras, R., Vespignani, A.: Large-scale topological and dynamical properties of the internet. Phys. Rev. E 65(6), 66130 (2002)CrossRef Vazquez, A., Pastor-Satorras, R., Vespignani, A.: Large-scale topological and dynamical properties of the internet. Phys. Rev. E 65(6), 66130 (2002)CrossRef
54.
Zurück zum Zitat Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393(6684), 440–442 (1998)CrossRef Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393(6684), 440–442 (1998)CrossRef
55.
Zurück zum Zitat White, J.G., Southgate, E., Thomson, J.N., Brenner, S.: The structure of the nervous system of the nematode Caenorhabditis elegans. Philos. Trans. R. Soc. Lond. B Biol. Sci. 314(1165), 1 (1986)CrossRef White, J.G., Southgate, E., Thomson, J.N., Brenner, S.: The structure of the nervous system of the nematode Caenorhabditis elegans. Philos. Trans. R. Soc. Lond. B Biol. Sci. 314(1165), 1 (1986)CrossRef
56.
Zurück zum Zitat Yerra, B.M., Levinson, D.M.: The emergence of hierarchy in transportation networks. Ann Reg. Sci. 39(3), 541–553 (2005)CrossRef Yerra, B.M., Levinson, D.M.: The emergence of hierarchy in transportation networks. Ann Reg. Sci. 39(3), 541–553 (2005)CrossRef
57.
Zurück zum Zitat Zegura, E.W., Calvert, K.L., Donahoo, M.J.: A quantitative comparison of graph-based models for internet topology. IEEE/ACM Trans. Netw. (TON) 5(6), 770–783 (1997) Zegura, E.W., Calvert, K.L., Donahoo, M.J.: A quantitative comparison of graph-based models for internet topology. IEEE/ACM Trans. Netw. (TON) 5(6), 770–783 (1997)
58.
Zurück zum Zitat Zhang, J., Ackerman, M.S., Adamic, L.: Expertise networks in online communities: structure and algorithms. In: Proceedings of the 16th international conference on World Wide Web, p. 230. ACM Press, New York (2007) Zhang, J., Ackerman, M.S., Adamic, L.: Expertise networks in online communities: structure and algorithms. In: Proceedings of the 16th international conference on World Wide Web, p. 230. ACM Press, New York (2007)
59.
Zurück zum Zitat Zhao, L., Lai, Y.C., Park, K., Ye, N.: Onset of traffic congestion in complex networks. Phys. Rev. E 71(2), 26125 (2005)CrossRef Zhao, L., Lai, Y.C., Park, K., Ye, N.: Onset of traffic congestion in complex networks. Phys. Rev. E 71(2), 26125 (2005)CrossRef
Metadaten
Titel
Structural Decompositions of Complex Networks
verfasst von
Rong Yang
Leyla Zhuhadar
Olfa Nasraoui
Copyright-Jahr
2012
Verlag
Springer London
DOI
https://doi.org/10.1007/978-1-4471-4048-1_6

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