# Analysis of a relationship triangle

##### January 12, 2011

In a model network of friends and foes, relationships will evolve until everyone becomes friendly or the network splits into two hostile factions, researchers suggest in the current issue of the Proceedings of the National Academy of Sciences.

Jon Kleinberg and colleagues used mathematics and to analyze an existing model that examined adages about relationship triangles, such as "the friend of my friend is my friend" and "the enemy of my friend is my enemy."

The researchers mathematically demonstrated that as the relationships within individual triangles changed in accordance with the model, the as a whole evolved either to a state of two intractably opposed camps, or to global harmony.

The end result depended upon the average extent of friendliness in the initial network.

The researchers applied their theoretical findings to actual historical events, including the split between Allied and Axis nations during World War II.

Using the countries' propensities to work together as a starting point, the model correctly predicted the eventual Allied-Axis alignment for all countries except Denmark and Portugal.

The model could help researchers determine the outcomes of other conflict-driven divisions, such as election races between opposing political parties or competition between two groups of companies in a common industry, the authors suggest.

Explore further: Mathematical model shows how groups split into factions

More information: "Analysis of a continuous-time model of structural balance," by Seth Marvel, Jon Kleinberg, Robert Kleinberg, and Steven Strogatz, Proceedings of the National Academy of Sciences.

## Related Stories

#### Mathematical model shows how groups split into factions

January 4, 2011

(PhysOrg.com) -- The school dance committee is split; one group wants an "Alice in Wonderland" theme; the other insists on "Vampire Jamboree." Mathematics could have predicted it.

#### Physics Model Determines Dynamics of Friends and Enemies

December 2, 2009

(PhysOrg.com) -- Sometimes friends can become enemies and enemies become friends, and it’s difficult to understand exactly how or why the changes took place. A new study shows that when the shifting of alliances and rivalries ...

#### 'The friend of my enemy is my enemy': Virtual universe study proves 80-year-old theory on how humans interact

July 19, 2010

A new study analysing interactions between players in a virtual universe game has for the first time provided large-scale evidence to prove an 80 year old psychological theory called Structural Balance Theory. The research, ...

#### The genes in your congeniality: Researchers identify genetic influence in social networks

January 26, 2009

Can't help being the life of the party? Maybe you were just born that way. Researchers from Harvard University and the University of California, San Diego have found that our place in a social network is influenced in part ...

#### Half of your friends lost in seven years

May 28, 2009

Had a good chat with someone recently? Has a good friend just helped you to do up your home? Then you will be lucky if that person still does that in seven years time. Sociologist Gerald Mollenhorst investigated how the context ...

#### Why New Political Parties Sizzle or Fizzle

August 4, 2008

(PhysOrg.com) -- Across the globe, new political parties, from green parties to anti-immigration parties, are constantly emerging in democratic countries. But while some of these nascent single-issue groups fade away, others, ...

## Recommended for you

#### Indonesian island found to be unusually rich in cave paintings

December 15, 2017

A tiny Indonesian island, previously unexplored by archaeologists, has been found to be unusually rich in ancient cave paintings following a study by researchers from The Australian National University (ANU).

#### Ancient feces reveal parasites described in earliest Greek medical texts

December 14, 2017

Ancient faeces from prehistoric burials on the Greek island of Kea have provided the first archaeological evidence for the parasitic worms described 2,500 years ago in the writings of Hippocrates - the most influential works ...

#### Coalition seeks to increase transparency on life science career prospects

December 14, 2017

Nine U.S. research universities and a major cancer institute today announced plans to give would-be life scientists clear, standardized data on graduate school admissions, education and training opportunities, and career ...

#### The oldest plesiosaur was a strong swimmer

December 14, 2017

Plesiosaurs were especially effective swimmers. These long extinct "paddle saurians" propelled themselves through the oceans by employing "underwater flight"—similar to sea turtles and penguins. Paleontologist from the ...

#### Experiments show Neolithic Thames beater could be used to kill a person

December 12, 2017

(Phys.org)—A team of researchers with the University of Edinburgh has found evidence that the "Thames Beater" was a weapon that could be used to kill another person—perhaps at times, with a single blow to the head. In ...

#### Averaging the wisdom of crowds

December 12, 2017

The best decisions are made on the basis of the average of various estimates, as confirmed by the research of Dennie van Dolder and Martijn van den Assem, scientists at VU Amsterdam. Using data from Holland Casino promotional ...