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:
A Glimpse at Paul G. Spirakis Read chapter Read first chapter

2015 | OriginalPaper | Chapter

On Some Combinatorial Properties of Random Intersection Graphs

Authors : Sotiris E. Nikoletseas, Christoforos L. Raptopoulos

Published in: Algorithms, Probability, Networks, and Games

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 consider a simple, yet general family of random graph models, namely Random Intersection Graphs (RIGs), which are motivated by applications in secure sensor networks, social networks and many more. In such models there is a universe \(\mathcal{M}\) of labels and each one of n vertices selects a random subset of \(\mathcal{M}\). Two vertices are connected if and only if their corresponding subsets of labels intersect. In particular, we briefly review the state of the art and we present key results from our research on the field, that highlight and take advantage of the intricacies and special structure of random intersection graphs. Finally, we present in more detail a particular result from our research, which concerns maximum cliques in the uniform random intersection graphs model (in which every vertex selects each label independently with some probability p), namely the Single Label Clique Theorem.

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 Of Concurrent Data Structures and Iterations
next chapter Efficient Equilibrium Concepts in Non-cooperative Network Formation
Footnotes
1
A perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph. Consequently, the clique number of a perfect graph is equal to its chromatic number.
 
Literature
1.
2.
Behrisch, M., Taraz, A., Ueckerdt, M.: Coloring random intersection graphs and complex networks. SIAM J. Discrete Math. 23, 288–299 (2008)MathSciNetCrossRefMATH
3.
Blackburn, S., Stinson, D., Upadhyay, J.: On the complexity of the herding attack and some related attacks on hash functions. Des. Codes Crypt. 64(1–2), 171–193 (2012)MathSciNetCrossRefMATH
4.
5.
6.
Deijfen, M., Kets, W.: Random intersection graphs with tunable degree distribution and clustering. Probab. Eng. Inform. Sci. 23, 661–674 (2009)MathSciNetCrossRefMATH
7.
Chan, H., Perrig, A., Song, D.: Random key predistribution schemes for sensor networks. In: Proceedings of the IEEE Symposium on Security and Privacy (2003)
8.
Efthymiou, C., Spirakis, P.G.: Sharp thresholds for Hamiltonicity in random intersection graphs. Theor. Comput. Sci. 411(40–42), 3714–3730 (2010)MathSciNetCrossRefMATH
9.
Fill, J.A., Sheinerman, E.R., Singer-Cohen, K.B.: Random intersection graphs when \(m = \omega (n)\): an equivalence theorem relating the evolution of the \(G(n, m, p)\) and \(G(n, p)\) models. Random Struct. Algorithms 16(2), 156–176 (2000)MathSciNetCrossRefMATH
10.
11.
Godehardt, E., Jaworski, J.: Two models of random intersection graphs for classification. In: Opitz, O., Schwaiger, M. (eds.) Exploratory Data Analysis in Empirical Research. Studies in Classification, Data Analysis, and Knowledge Organization, pp. 67–82. Springer, Heidelberg (2002)
12.
Karoński, M., Sheinerman, E.R., Singer-Cohen, K.B.: On random intersection graphs: the subgraph problem. Comb. Probab. Comput. j. 8, 131–159 (1999)MathSciNetCrossRefMATH
13.
14.
Nikoletseas, S., Raptopoulos, C., Spirakis, P.G.: Colouring non-sparse random intersection graphs. In: Královič, R., Niwiński, D. (eds.) MFCS 2009. LNCS, vol. 5734, pp. 600–611. Springer, Heidelberg (2009) CrossRef
15.
Nikoletseas, S., Raptopoulos, C., Spirakis, P.G.: Expander properties and the cover time of random intersection graphs. Theor. Comput. Sci. 410(50), 5261–5272 (2009)MathSciNetCrossRefMATH
16.
Nikoletseas, S., Raptopoulos, C., Spirakis, P.G.: Large independent sets in general random intersection graphs. Theor. Comput. Sci. 406, 215–224 (2008)MathSciNetCrossRefMATH
17.
Nikoletseas, S., Raptopoulos, C., Spirakis, P.G.: Maximum cliques in graphs with small intersection number and random intersection graphs. In: Rovan, B., Sassone, V., Widmayer, P. (eds.) MFCS 2012. LNCS, vol. 7464, pp. 728–739. Springer, Heidelberg (2012) CrossRef
18.
Nikoletseas, S., Raptopoulos, C., Spirakis, P.G.: On the independence number and hamiltonicity of uniform random intersection graphs. Theor. Comput. Sci. 412(48), 6750–6760 (2011)MathSciNetCrossRefMATH
19.
Molloy, M., Reed, B.: Graph Colouring and the Probabilistic Method. Springer, Heidelberg (2002)CrossRefMATH
20.
Raptopoulos, C., Spirakis, P.G.: Simple and efficient greedy algorithms for hamilton cycles in random intersection graphs. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 493–504. Springer, Heidelberg (2005) CrossRef
21.
22.
23.
Singer-Cohen, K.B.: Random Intersection Graphs. Ph.D. thesis, John Hopkins University (1995)
24.
25.
26.
27.
Zhao, J., Yağan, O., Gligor, V.: On the strengths of connectivity and robustness in general random intersection graphs. In: Proceedings of the IEEE Conference on Decision and Control (CDC), December 2014
Metadata
Title
On Some Combinatorial Properties of Random Intersection Graphs
Authors
Sotiris E. Nikoletseas
Christoforos L. Raptopoulos
Copyright Year
2015
Book
Algorithms, Probability, Networks, and Games

Print ISBN: 978-3-319-24023-7

Electronic ISBN: 978-3-319-24024-4

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-24024-4_21

Premium Partner

    Image Credits