Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Robustness of Spatial Preferential Attachment Networks Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Local Clustering Coefficient in Generalized Preferential Attachment Models

Authors : Alexander Krot, Liudmila Ostroumova Prokhorenkova

Published in: Algorithms and Models for the Web Graph

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper, we analyze the local clustering coefficient of preferential attachment models. A general approach to preferential attachment was introduced in [19], where a wide class of models (PA-class) was defined in terms of constraints that are sufficient for the study of the degree distribution and the clustering coefficient. It was previously shown that the degree distribution in all models of the PA-class follows a power law. Also, the global clustering coefficient was analyzed and a lower bound for the average local clustering coefficient was obtained. We expand the results of [19] by analyzing the local clustering coefficient for the PA-class of models. Namely, we analyze the behavior of C(d) which is the average local clustering for the vertices of degree d.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Robustness of Spatial Preferential Attachment Networks
next chapter Hyperbolicity, Degeneracy, and Expansion of Random Intersection Graphs
Literature
1.
Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)CrossRefMATH
2.
Bansal, S., Khandelwal, S., Meyers, L.A.: Exploring biological network structure with clustered random networks. BMC Bioinf. 10, 405 (2009)CrossRef
3.
Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Sci. 286(5439), 509–512 (1999)CrossRef
4.
Barabási, A.-L., Albert, R., Jeong, H.: Mean-field theory for scale-free random networks. Phys. A 272(1–2), 173–187 (1999)CrossRef
5.
Albert, R., Jeong, H., Barabási, A.-L.: Internet: diameter of the world-wide web. Nat. 401, 130–131 (1999)CrossRef
6.
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Complex networks: structure and dynamics. Phys. Rep. 424(45), 175–308 (2006)CrossRefMathSciNet
7.
Bollobás, B., Riordan, O.M.: Mathematical results on scale-free random graphs. In: Handbook of Graphs and Networks: From the Genome to the Internet (2003)
8.
Bollobás, B., Riordan, O.M., Spencer, J., Tusnády, G.: The degree sequence of a scale-free random graph process. Random Struct. Algorithms 18(3), 279–290 (2001)CrossRefMATH
9.
Borgs, C., Brautbar, M., Chayes, J., Khanna, S., Lucier, B.: The power of local information in social networks. Preprint (2012)
10.
Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A., Wiener, J.: Graph structure in the web. Comput. Netw. 33(16), 309–320 (2000)CrossRef
11.
Buckley, P.G., Osthus, D.: Popularity based random graph models leading to a scale-free degree sequence. Discrete Math. 282, 53–63 (2004)CrossRefMathSciNetMATH
12.
Catanzaro, M., Caldarelli, G., Pietronero, L.: Assortative model for social networks. Phys. Rev. E 70, 037101 (2004)CrossRef
13.
Leskovec, J.: Dynamics of large networks. ProQuest (2008)
14.
Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the internet topology. In: Proceedings of SIGCOMM (1999)
15.
16.
Holme, P., Kim, B.J.: Growing scale-free networks with tunable clustering. Phys. Rev. E 65(2), 026107 (2002)CrossRef
17.
Newman, M.E.J.: Pareto distributions and Zipf’s law. Contemp. Phys. 46(5), 323–351 (2005)CrossRef
18.
19.
Ostroumova, L., Ryabchenko, A., Samosvat, E.: Generalized preferential attachment: tunable power-law degree distribution and clustering coefficient. In: Bonato, A., Mitzenmacher, M., Prałat, P. (eds.) WAW 2013. LNCS, vol. 8305, pp. 185–202. Springer, Heidelberg (2013) CrossRef
20.
Ravasz, E., Barabási, A.-L.: Hierarchical organization in complex networks. Phys. Rev. E 67(2), 26112 (2003)CrossRef
21.
22.
Serrano, M.A., Boguñá, M.: Clustering in complex networks. II. Percolation properties. Phys. Rev. E 74, 056115 (2006)CrossRefMathSciNet
23.
Vázquez, A., Pastor-Satorras, R., Vespignani, A.: Large-scale topological and dynamical properties of the internet. Phys. Rev. E 65, 066130 (2002)CrossRef
24.
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)CrossRef
25.
Zhou, T., Yan, G., Wang, B.-H.: Maximal planar networks with large clustering coefficient and power-law degree distribution. Phys. Rev. E 71(4), 046141 (2005)CrossRef
Metadata
Title
Local Clustering Coefficient in Generalized Preferential Attachment Models
Authors
Alexander Krot
Liudmila Ostroumova Prokhorenkova
Copyright Year
2015
Book
Algorithms and Models for the Web Graph

Print ISBN: 978-3-319-26783-8

Electronic ISBN: 978-3-319-26784-5

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-26784-5_2

Premium Partner

    Image Credits