National Academy Science Letters

, Volume 41, Issue 4, pp 233–238 | Cite as

On the Properties of Square Signed Graph

  • Deepa SinhaEmail author
  • Deepakshi Sharma
Short Communication


Social network analysis has been a subject of interest to many sociologists, computer scientists, psychologists and mathematicians for many centuries now. Lately another aspect of the social network, specific kind of links (friendship/enmity, trust/distrust, like/dislike) has been studied vigorously. In this paper, we try to explore and analyse these networks mathematically by taking a small subnetwork and predicting its properties and behaviour. Let \(G=(V,E)\) be a graph then square graph of G is obtained by adding to G edges which connect pairs of vertices of G at a distance two apart. In this paper we discuss few properties of square signed graphs along with their algorithms.


Social network Signed social network Signed graph Marked signed graph Square signed graph Closed neighborhood Sign-compatibility Signed-regularity Clusterability Algorithm 



Authors wish to thank Prof Mukti Acharya and the referees for going through the paper for the suggestions and improvement of the paper.


  1. 1.
    Harary F (1969) Graph theory. Addision Wesley, ReadingCrossRefzbMATHGoogle Scholar
  2. 2.
    West DB (2001) Introduction to graph theory, vol 2. Prentice Hall, Upper Saddle RiverGoogle Scholar
  3. 3.
    Zaslavsky T (2012) A mathematical bibliography of signed and gain graphs and allied areas. Electron J Combin 1000:8MathSciNetGoogle Scholar
  4. 4.
    Cartwright D, Harary F (1956) Structural balance: a generalization of Heider’s theory. Psychol Rev 63(5):277CrossRefPubMedGoogle Scholar
  5. 5.
    Zaslavsky T (1982) Signed graph coloring. Discret Math 39(2):215–228MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Mukhopadhyay A (1967) The square root of a graph. J Combin Theory 2(3):290–295MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Sinha D, Garg P (2011) On the regularity of some signed graph structures. AKCE Int J Graphs Combin 8(1):63–74MathSciNetzbMATHGoogle Scholar
  8. 8.
    Zaslavsky T (1991) Orientation of signed graphs. Eur J Combin 12(4):361–375MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Sinha D, Dhama A (2013) Sign-compatibility of some derived signed graphs. Indian J Math 55(1):23–40MathSciNetzbMATHGoogle Scholar
  10. 10.
    Sinha D, Sethi A (2015) An optimal algorithm to detect sign compatibility of a given sigraph. Natl Acad Sci Lett 38(3):235–238MathSciNetCrossRefGoogle Scholar
  11. 11.
    Doreian P, Mrvar A (2009) Partitioning signed social networks. Soc Netw 31(1):1–11CrossRefzbMATHGoogle Scholar
  12. 12.
    Davis JA (1967) Clustering and structural balance in graphs. Hum Relat 20(2):181–187CrossRefGoogle Scholar
  13. 13.
    Yang B, Cheung WK, Liu J (2007) Community mining from signed social networks. IEEE Trans Knowl Data Eng 19(10):1333–1348CrossRefGoogle Scholar
  14. 14.
    Leskovec J, Huttenlocher D, Kleinberg J (2010) Signed networks in social media. In: Proceedings of the SIGCHI conference on human factors in computing systems. ACM, pp 1361–1370Google Scholar
  15. 15.
    Sinha D, Sethi A (2017) An optimal algorithm to detect clusterability of a given sigraph. ManuscriptGoogle Scholar
  16. 16.
    Sinha D, Sharma D (2017) Algorithm characterization of square signed graph and its balance property (Preprint) Google Scholar

Copyright information

© The National Academy of Sciences, India 2018

Authors and Affiliations

  1. 1.Department of MathematicsSouth Asian UniversityNew DelhiIndia

Personalised recommendations