Structural Balance Considerations for Networks with Preference Orders as Node Attributes

Olle Abrahamsson; Danyo Danev; Erik G. Larsson

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arXiv · 2210.01858

Structural Balance Considerations for Networks with Preference Orders as Node Attributes

Olle Abrahamsson·Danyo Danev·Erik G. Larsson

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Abstract

We discuss possible definitions of structural balance conditions in a network with preference orderings as node attributes. The main result is that for the case with three alternatives ($A,B,C$) we reduce the $(3!)^3 = 216$ possible configurations of triangles to $10$ equivalence classes, and use these as measures of balance of a triangle towards possible extensions of structural balance theory. Moreover, we derive a general formula for the number of equivalent classes for preferences on $n$ alternatives. Finally, we analyze a real-world data set and compare its empirical distribution of triangle equivalence classes to a null hypothesis in which preferences are randomly assigned to the nodes.

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Olle Abrahamsson, Danyo Danev, Erik G. Larsson. 2022-10-04. Structural Balance Considerations for Networks with Preference Orders as Node Attributes. https://arxiv.org/abs/2210.01858

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