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In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is positive. The name "signed graph" and the notion of balance appeared first in a mathematical paper of Frank Harary in 1953. Dénes Kőnig had already studied equivalent notions in 1936 under a different terminology but without recognizing the relevance of the sign group.At the Center for Group Dynamics at the University of Michigan, Dorwin Cartwright and Harary generalized Fritz Heider's psychological theory of balance in triangles of sentiments to a psychological theory of balance in signed graphs.

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rdfs:label	Grafo signado (es) 부호형 그래프 (ko) Signed graph (en)
rdfs:comment	En teoría de grafos, un grafo signado o grafo con signos es un grafo cuyas aristas tienen un signo positivo o negativo, que puede representar cualquier relación dicotómica. Estos grafos cumplen con la propiedad de dualidad antitética, de modo que el dual de un grafo signado implica cambiar el signo de sus aristas. Además, el dual del dual de un grafo signado, vuelve a restablecer las aristas a sus signos originales. (es) 그래프 이론에서 부호형 그래프(signed graph)란 각 변(edge)이 양부호나 음부호를 가지는 그래프를 의미한다. (ko) In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is positive. The name "signed graph" and the notion of balance appeared first in a mathematical paper of Frank Harary in 1953. Dénes Kőnig had already studied equivalent notions in 1936 under a different terminology but without recognizing the relevance of the sign group.At the Center for Group Dynamics at the University of Michigan, Dorwin Cartwright and Harary generalized Fritz Heider's psychological theory of balance in triangles of sentiments to a psychological theory of balance in signed graphs. (en)
foaf:depiction
dct:subject	Matroid theory Extensions and generalizations of graphs Oriented matroids
Wikipage page ID	2472618 (xsd:integer)
Wikipage revision ID	1117775260 (xsd:integer)
Link from a Wikipage to another Wikipage	Matroid theory Biased graph Cycle (graph theory) University of Michigan Complete graph Extensions and generalizations of graphs Mathematics Chromatic polynomial Frank Harary Graph (discrete mathematics) Graph coloring NP-hard Correlation clustering Oriented matroids Colored matroid Fritz Heider Path (graph theory) Petri net Marked graph Matroid Gain graph Dénes Kőnig First World War Balance theory Directed graph Graph theory Ising model Knot theory Social dynamics Spin glass Ground state Bidirected graph Bipartite graph The enemy of my enemy is my friend Dorwin Cartwright Group theory Maxcut Root system Social psychology Vertex (graph theory) Topological graph theory Signed graphs Accademia Nazionale dei Lincei Matroid theory
Link from a Wikipage to an external page	http://www.combinatorics.org/ojs/index.php/eljc/article/view/DS8
sameAs	Signed graph Signed graph Signed graph Signed graph Signed graph Signed graph
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thumbnail	wiki-commons:Special:FilePath/Pox.jpg?width=300
has abstract	En teoría de grafos, un grafo signado o grafo con signos es un grafo cuyas aristas tienen un signo positivo o negativo, que puede representar cualquier relación dicotómica. Estos grafos cumplen con la propiedad de dualidad antitética, de modo que el dual de un grafo signado implica cambiar el signo de sus aristas. Además, el dual del dual de un grafo signado, vuelve a restablecer las aristas a sus signos originales. (es) In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is positive. The name "signed graph" and the notion of balance appeared first in a mathematical paper of Frank Harary in 1953. Dénes Kőnig had already studied equivalent notions in 1936 under a different terminology but without recognizing the relevance of the sign group.At the Center for Group Dynamics at the University of Michigan, Dorwin Cartwright and Harary generalized Fritz Heider's psychological theory of balance in triangles of sentiments to a psychological theory of balance in signed graphs. Signed graphs have been rediscovered many times because they come up naturally in many unrelated areas. For instance, they enable one to describe and analyze the geometry of subsets of the classical root systems. They appear in topological graph theory and group theory. They are a natural context for questions about odd and even cycles in graphs. They appear in computing the ground state energy in the non-ferromagnetic Ising model; for this one needs to find a largest balanced edge set in Σ. They have been applied to data classification in correlation clustering. (en) 그래프 이론에서 부호형 그래프(signed graph)란 각 변(edge)이 양부호나 음부호를 가지는 그래프를 의미한다. (ko)
gold:hypernym	Graph
prov:wasDerivedFrom	wikipedia-en:Signed_graph?oldid=1117775260&ns=0
page length (characters) of wiki page	23641 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Signed_graph
is Link from a Wikipage to another Wikipage of	Bipartite double cover Biased graph Degree (graph theory) Incidence matrix Interpersonal ties Robert Abelson Social network Social network analysis Trace diagram Frank Harary Geometrical frustration Graph coloring Sign (mathematics) Cluster analysis Colored matroid

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