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Generation of Simple, Connected, Non-isomorphic Random Graphs

  • Maumita ChakrabortyEmail author
  • Sumon Chowdhury
  • Rajat Kumar Pal
Chapter
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 995)

Abstract

In graph theory, generation of random graphs finds a wide range of applications in different scheduling problems, approximation algorithms, problems involving modeling and simulation, different database applications, and obviously to test the performance of any algorithm. The algorithm, which has been devised in this paper, is mainly for the purpose of providing test bed for checking performance of other algorithms. It generates different non-isomorphic graph instances of a given order and having unique number of edges. The number of such instances possible for a graph of given order has also been subsequently formulated. Different such graph instances of different orders, generated in a uniform computing environment, and the computing time required for such generations have also been included in this paper. The simplicity and efficiency of the algorithm, subsequently proved in the paper, give us a new insight in the area of random graph generation and have called for further research scope in the domain.

Keywords

Random graph Non-isomorphic graph Connected graph Graph generation 

References

  1. 1.
    Aho, A.V., Hopcroft, J.E., Ullman, J.D.: Data Structures and Algorithms. First Edition. Pearson (1983)Google Scholar
  2. 2.
    Bayati, M., Kim, J.H., Saberi, A.: A sequential algorithm for generating random graphs. Algorithmica (Springer) 58(4), 860–910 (2010)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bhuiyan, H., Khan, M., Marathe, M.: A parallel algorithm for generating a random graph with a prescribed degree sequence. In: arXiv preprint: 1708.07290 (2017)Google Scholar
  4. 4.
    Cordeiro, D., Mounie, G., Perarnau, S., Trystram, D., Vincent, J.M., Wagner, F.: Random graph generation for scheduling simulations. In: Proceedings of Third International Conference on Simulation Tools and Techniques (SIMUTools’10), Article No. 60 (2010)Google Scholar
  5. 5.
    Deo, N.: Graph Theory with Applications to Engineering and Computer Science. Prentice Hall of India Pvt. Ltd., New Delhi (2003)zbMATHGoogle Scholar
  6. 6.
    Erdos, P., Renyi, A.: On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5, 17–61 (1960)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Horn, M.V., Richter, A., Lopez, D.: A random graph generator. In: Proceedings of 36th Annual Midwest Instruction and Computing Symposium, Duluth, Minnesota (2003)Google Scholar
  8. 8.
    Horowitz, E., Sahni, S., Anderson, S.: Fundamentals of Data Structures in C, 2nd edn. Universities Press Pvt. Ltd., Hyderabad, India (2008)zbMATHGoogle Scholar
  9. 9.
    Nobari, S., Lu, X., Karras, P., Bressan, S.: Fast random graph generation. In: Proceedings of the 14th International Conference on Extending Database Technology, Uppsala, Sweden, pp. 331–342 (2011).  https://doi.org/10.1145/1951365.1951406
  10. 10.
    Viger, F., Latapy, M.: Efficient and simple generation of random simple connected graphs with prescribed degree sequence. In: Computing and Combinatorics, COCOON 2005. Lecture Notes in Computer Science (Springer, Berlin, Heidelberg) 3595, pp. 440–449 (2005).  https://doi.org/10.1007/11533719_4Google Scholar
  11. 11.
    Viger, F., Latapy, M.: Efficient and simple generation of random simple connected graphs with prescribed degree sequence. J. Complex Netw. 4(1), 15–37 (2016)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Wang, C., Lizardo, O., Hachen, D.: Algorithms for generating large-scale clustered random graphs. Network Sci. 2, 403–415 (2014)CrossRefGoogle Scholar
  13. 13.
    Weisstein, E.W.: (IG) isomorphic graphs. In: MathWorld—A Wolfram Web Resource. http://mathworld.wolfram.com/IsomorphicGraphs.html. Accessed 18 Jan 2019
  14. 14.
    Weisstein, E.W.: (RG) random graph. In: MathWorld—A Wolfram Web Resource. http://math-world.wolfram.com/RandomGraph.html. Accessed 18 Jan 2019
  15. 15.
    Wikipedia (ST) Spanning Tree. https://en.wikipedia.org/wiki/Spanning_tree. Accessed 18 Jan 2019

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Maumita Chakraborty
    • 1
    Email author
  • Sumon Chowdhury
    • 2
  • Rajat Kumar Pal
    • 3
  1. 1.Department of Information TechnologyInstitute of Engineering and ManagementKolkataIndia
  2. 2.Tata Consultancy ServicesKolkataIndia
  3. 3.Department of Computer Science and EngineeringUniversity of CalcuttaKolkataIndia

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