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Signed Graphs

  • Reference work entry
  • First Online:
Encyclopedia of Social Network Analysis and Mining

  • 184 Accesses

Synonyms

Biased graph; Gain graph; Signed network

Glossary

Arc:

An ordered pair of nodes adjacent in the graph

Cycle:

A loop of at least three nodes in which the first and the last nodes 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 entities called 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 = {n 1,…n m } and a set of edges E = {e 1,…, e n }, where each edge is a set...

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Recommended Reading

  • Signed graphs are covered thoroughly in the literature, both from the theoretic and application angles. A good starting point is a general book on graph theory, such as excellent text by Harary (1969) or Bondy and Murty (2002). An approach focusing more on the social aspects of networks is presented by famous textbooks by Wasserman and Faust (1994) and Newman (2010).

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  • A very detailed summary of social balance research covering over 200 different papers is presented by Taylor (1970). Readers interested in a more anthropological approach to the study of social structure and balance should consult (Hage and Harary 1983). Our discussion on balance in social structures can be further extended to the notion of clusterability. Concepts of clusterability, ranked clusterability, and transitive tournaments are discussed at length by Holland and Leinhardt (1971).

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  • If readers desire to investigate mathematical properties of signed graphs, they are advised to follow the work of Zaslavsky (1981). For the most comprehensive analysis of signed graphs literature, the reader is encouraged to study the bibliography compiled by Zaslavsky (1998).

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Author information

Authors and Affiliations

  1. Institute of Computing Science, Poznan' University of Technology, Poznań, Poland

    Stefaniak Krzysztof & Morzy Mikołaj

Authors
  1. Stefaniak Krzysztof
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  2. Morzy Mikołaj
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Calgary, Calgary, AB, Canada

    Reda Alhajj

  2. Department of Computer Science, University of Calgary, Calgary, AB, Canada

    Jon Rokne

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Krzysztof, S., Mikołaj, M. (2014). Signed Graphs. In: Alhajj, R., Rokne, J. (eds) Encyclopedia of Social Network Analysis and Mining. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6170-8_251

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