Encyclopedia of Social Network Analysis and Mining

2018 Edition
| Editors: Reda Alhajj, Jon Rokne

Signed Graphs

  • Krzysztof Stefaniak
  • Mikołaj Morzy
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-7131-2_251

Synonyms

Glossary

Arc

An ordered pair of nodes adjacent in the graph

Cycle

A loop of at least three nodes in which the first node and the last node are the same

Digraph

A graph in which all relations are directed

Dyad

A pair of nodes and the incidence relation between them

Edge

A pair of nodes adjacent in the graph

Graph

A data structure consisting of a set of nodes, and a set of pairs of nodes, called edges or arcs

Loop

A walk in the graph in which all edges are distinct

Path

A walk in the graph in which all edges and nodes are distinct

Sociomatrix

Representation of the incidence relation as a two-dimensional matrix in which rows and columns represent nodes, and cells represent relation values

Triad

A triple of nodes and all incidence relations between them

Valence

Semantic orientation of an edge in a signed graph

Definition

Given a set of nodes N = {n1,..., nm} and a set of edges E = {e1,..., en}, where each edge is a pair of nodes, ek = (n

This is a preview of subscription content, log in to check access.

References

  1. Anchuri P, Magdon-Ismail M (2012) Communities and balance in signed networks: a spectral approach. In: Advances in social networks analysis and mining (ASONAM), 2012 IEEE/ACM international conference on IEEE, pp 235–242Google Scholar
  2. Antal T, Krapivsky P, Redner S (2006) Social balance on networks: the dynamics of friendship and enmity. Physica D 224(1–2):130–136. Dynamics on Complex Networks and ApplicationsMathSciNetzbMATHCrossRefGoogle Scholar
  3. Bondy AJ, Murty USR (2002) Graph theory with applications. Wiley, New YorkzbMATHGoogle Scholar
  4. Brzozowski MJ, Hogg T, Szabo G (2008) Friends and foes: ideological social networking. In: Proceedings of the twenty-sixth annual SIGCHI conference on human factors in computing systems, CHI ‘08, ACM, New York, pp 817–820Google Scholar
  5. Cartwright D, Gleason T (1966) The number of paths and cycles in a digraph. Psychometrika 31(2):179–199MathSciNetzbMATHCrossRefGoogle Scholar
  6. Cartwright D, Harary F (1956) Structural balance: a generalization of Heider’s theory. Psychol Rev 63(5):277–293CrossRefGoogle Scholar
  7. Davis JA (1967) Clustering and structural balance in graphs. Hum Relat 20(2):181–187CrossRefGoogle Scholar
  8. Doreian P (2017) Reflections on studying signed networks. J Interdiscip Methodol Issues Sci 2:3.1–3.16Google Scholar
  9. Guha R, Kumar R, Raghavan P, Tomkins A (2004) Propagation of trust and distrust. In: Proceedings of the 13th international conference on World Wide Web, WWW’04, ACM, New York, pp 403–412Google Scholar
  10. Hage P (1979) Graph theory as a structural model in cultural anthropology. Annu Rev Anthropol 8:115–136CrossRefGoogle Scholar
  11. Hage P, Harary F (1983) Structural models in anthropology. Cambridge University Press, Cambridge, MAzbMATHGoogle Scholar
  12. Harary F (1953) On the notion of balance of a signed graph. Mich Math J 2(2):143–146MathSciNetzbMATHCrossRefGoogle Scholar
  13. Harary F (1956) Structural models: an introduction to the theory of directed graphs. Wiley, New YorkGoogle Scholar
  14. Harary F (1959) On the measurement of structural balance. Behav Sci 4(4):316–323MathSciNetCrossRefGoogle Scholar
  15. Harary F (1960) A matrix criterion for structural balance. Nav Res Logist Q 7(2):195–199zbMATHCrossRefGoogle Scholar
  16. Harary F (1961) A structural analysis of the situation in the middle east in 1956. J Confl Resolut 5(2):167–178CrossRefGoogle Scholar
  17. Harary F (1969) Graph theory. Addison-Wesley, ReadingzbMATHCrossRefGoogle Scholar
  18. Heider F (1946) Attitudes and cognitive organization. J Psychol 21(2):107–112CrossRefGoogle Scholar
  19. Holland PW, Leinhardt S (1971) Transitivity in structural models of small groups. Small Group Res 2(2):107–124Google Scholar
  20. Ilany A, Barocas A, Koren L, Kam M, Geffen E (2013) Structural balance in the social networks of a wild mammal. Anim Behav 85(6):1397–1405CrossRefGoogle Scholar
  21. Kunegis J, Lommatzsch A, Bauckhage C (2009) The slashdot zoo: mining a social network with negative edges. In: Proceedings of the 18th international conference on World Wide Web, WWW’09, ACM, New York, pp 741–750Google Scholar
  22. Kunegis J, Schmidt S, Lommatzsch A, Lerner J, De Luca EW, Albayrak S (2010) Spectral analysis of signed graphs for clustering, prediction and visualization. In: Proceedings of the 2010 SIAM international conference on data mining, SIAM, pp 559–570Google Scholar
  23. Leskovec J, Huttenlocher D, Kleinberg J (2010a) Predicting positive and negative links in online social networks. In: Proceedings of the 19th international conference on World Wide Web, WWW’10, ACM, New York, pp 641–650Google Scholar
  24. Leskovec J, Huttenlocher D, Kleinberg J (2010b) Signed networks in social media. In: Proceedings of the SIGCHI conference on human factors in computing systems, ACM, pp 1361–1370Google Scholar
  25. Maniu S, Cautis B, Abdessalem T (2011) Building a signed network from interactions in wikipedia. In: Databases and social networks, ACM, pp 19–24Google Scholar
  26. Moore M (1979) Structural balance and international relations. Eur J Soc Psychol 9(3):323–326CrossRefGoogle Scholar
  27. Newman M (2010) Networks: an introduction. Oxford University Press, New YorkzbMATHCrossRefGoogle Scholar
  28. Norman R, Roberts F (1972) A derivation of a measure of relative balance for social structures and a characterization of extensive ratio systems. J Math Psychol 9(1):66–91MathSciNetzbMATHCrossRefGoogle Scholar
  29. Proskurnikov AV, Matveev AS, Cao M (2016) Opinion dynamics in social networks with hostile camps: consensus vs. polarization. IEEE Trans Autom Control 61(6):1524–1536MathSciNetzbMATHCrossRefGoogle Scholar
  30. Sampson S (1968) A novitiate in a period of change: an experimental and case study of relationship. PhD thesis, Cornell UniversityGoogle Scholar
  31. Shi G, Proutiere A, Johansson M, Baras JS, Johansson KH (2016) The evolution of beliefs over signed social networks. Oper Res 64(3):585–604MathSciNetzbMATHCrossRefGoogle Scholar
  32. Tang J, Chang S, Aggarwal C, Liu H (2015) Negative link prediction in social media. In: Proceedings of the eighth ACM international conference on web search and data mining, ACM, pp 87–96Google Scholar
  33. Tang J, Chang Y, Aggarwal C, Liu H (2016) A survey of signed network mining in social media. ACM Comput Surv (CSUR) 49(3):42CrossRefGoogle Scholar
  34. Taylor HF (1970) Balance in small groups. Van Nostrand Reinhold Co, New YorkGoogle Scholar
  35. Trinajstic N (1983) Chemical graph theory. CRC Press, Boca RatonGoogle Scholar
  36. Wasserman S, Faust K (1994) Social network analysis: methods and applications (structural analysis in the social sciences). Structural analysis in the social sciences, 1st edn. Cambridge University Press, Cambridge, MAzbMATHCrossRefGoogle Scholar
  37. Wu Z, Aggarwal CC, Sun J (2016) The troll-trust model for ranking in signed networks. In: Proceedings of the ninth ACM international conference on web search and data mining, ACM, pp 447–456Google Scholar
  38. Yang B, Cheung W, Liu J (2007a) Community mining from signed social networks. IEEE Trans Knowl Data Eng 19(10)Google Scholar
  39. Yang B, Cheung W, Liu J (2007b) Community mining from signed social networks. IEEE Trans Knowl Data Eng 19(10):1333–1348CrossRefGoogle Scholar
  40. Yang SH, Smola AJ, Long B, Zha H, Chang Y (2012) Friend or frenemy?: predicting signed ties in social networks. In: Proceedings of the 35th international ACM SIGIR conference on Research and development in information retrieval, ACM, pp 555–564Google Scholar
  41. Yu T, Bai L, Guo J, Yang Z (2016) Construct a bipartite signed network in youtube. Big data: concepts, methodologies, tools, and applications: concepts, methodologies, tools, and applications, IGI Global, Hershey, PA, pp 370Google Scholar
  42. Zaslavsky T (1981) Characterizations of signed graphs. J Graph Theory 5(4):401–406MathSciNetzbMATHCrossRefGoogle Scholar
  43. Zaslavsky T (1982) Signed graphs. Discret Appl Math 4(1):47–74MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Computing SciencePoznan University of TechnologyPoznańPoland

Section editors and affiliations

  • Przemyslaw Kazienko
    • 1
  • Jaroslaw Jankowski
    • 2
  1. 1.Faculty of Computer Science and Management, Department of Computational IntelligenceWroclaw University of Science and TechnologyWrocławPoland
  2. 2.Faculty of Computer Science and Information TechnologyWest Pomeranian University of TechnologySzczecinPoland