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...
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References
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 235–242
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 Applications
Bondy AJ, Murty USR (2002) Graph theory with applications. Wiley, New York
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 817–820
Cartwright D, Gleason T (1966) The number of paths and cycles in a digraph. Psychometrika 31(2):179–199
Cartwright D, Harary F (1956) Structural balance: a generalization of Heider’s theory. Psychol Rev 63(5):277–293
Davis JA (1967) Clustering and structural balance in graphs. Hum Relat 20(2):181–187
Doreian P (2017) Reflections on studying signed networks. J Interdiscip Methodol Issues Sci 2:3.1–3.16
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 403–412
Hage P (1979) Graph theory as a structural model in cultural anthropology. Annu Rev Anthropol 8:115–136
Hage P, Harary F (1983) Structural models in anthropology. Cambridge University Press, Cambridge, MA
Harary F (1953) On the notion of balance of a signed graph. Mich Math J 2(2):143–146
Harary F (1956) Structural models: an introduction to the theory of directed graphs. Wiley, New York
Harary F (1959) On the measurement of structural balance. Behav Sci 4(4):316–323
Harary F (1960) A matrix criterion for structural balance. Nav Res Logist Q 7(2):195–199
Harary F (1961) A structural analysis of the situation in the middle east in 1956. J Confl Resolut 5(2):167–178
Harary F (1969) Graph theory. Addison-Wesley, Reading
Heider F (1946) Attitudes and cognitive organization. J Psychol 21(2):107–112
Holland PW, Leinhardt S (1971) Transitivity in structural models of small groups. Small Group Res 2(2):107–124
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):1397–1405
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 741–750
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 559–570
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 641–650
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 1361–1370
Maniu S, Cautis B, Abdessalem T (2011) Building a signed network from interactions in wikipedia. In: Databases and social networks, ACM, pp 19–24
Moore M (1979) Structural balance and international relations. Eur J Soc Psychol 9(3):323–326
Newman M (2010) Networks: an introduction. Oxford University Press, New York
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):66–91
Proskurnikov AV, Matveev AS, Cao M (2016) Opinion dynamics in social networks with hostile camps: consensus vs. polarization. IEEE Trans Autom Control 61(6):1524–1536
Sampson S (1968) A novitiate in a period of change: an experimental and case study of relationship. PhD thesis, Cornell University
Shi G, Proutiere A, Johansson M, Baras JS, Johansson KH (2016) The evolution of beliefs over signed social networks. Oper Res 64(3):585–604
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 87–96
Tang J, Chang Y, Aggarwal C, Liu H (2016) A survey of signed network mining in social media. ACM Comput Surv (CSUR) 49(3):42
Taylor HF (1970) Balance in small groups. Van Nostrand Reinhold Co, New York
Trinajstic N (1983) Chemical graph theory. CRC Press, Boca Raton
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, MA
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 447–456
Yang B, Cheung W, Liu J (2007a) Community mining from signed social networks. IEEE Trans Knowl Data Eng 19(10)
Yang B, Cheung W, Liu J (2007b) Community mining from signed social networks. IEEE Trans Knowl Data Eng 19(10):1333–1348
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 555–564
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 370
Zaslavsky T (1981) Characterizations of signed graphs. J Graph Theory 5(4):401–406
Zaslavsky T (1982) Signed graphs. Discret Appl Math 4(1):47–74
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Stefaniak, K., Morzy, M. (2018). Signed Graphs. In: Alhajj, R., Rokne, J. (eds) Encyclopedia of Social Network Analysis and Mining. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-7131-2_251
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