Measuring partial balance in signed networks. Aref, S. & Wilson, M. C. Journal of Complex Networks, 6(4):566-595, Oxford University Press, 2018.
Measuring partial balance in signed networks [link]Paper  abstract   bibtex   3 downloads  
Is the enemy of an enemy necessarily a friend? If not, to what extent does this tend to hold? Such questions were formulated in terms of signed (social) networks and necessary and sufficient conditions for a network to be ‘balanced’ were obtained around 1960. Since then the idea that signed networks tend over time to become more balanced has been widely used in several application areas. However, investigation of this hypothesis has been complicated by the lack of a standard measure of partial balance, since complete balance is almost never achieved in practice. We formalize the concept of a measure of partial balance, discuss various measures, compare the measures on synthetic datasets and investigate their axiomatic properties. The synthetic data involves Erdős-Rényi and specially structured random graphs. We show that some measures behave better than others in terms of axioms and ability to differentiate between graphs. We also use well-known data sets from the sociology and biology literature, such as Read's New Guinean tribes, gene regulatory networks related to two organisms, and a network involving senate bill co-sponsorship. Our results show that substantially different levels of partial balance is observed under cycle-based, eigenvalue-based and frustration-based measures. We make some recommendations for measures to be used in future work.
@article{aref2018measuring,
  title={Measuring partial balance in signed networks},
  author={Aref, Samin and Wilson, Mark C.},
  journal={Journal of Complex Networks},
  volume={6},
  number={4},
  pages={566-595},
  year={2018},
  publisher={Oxford University Press},
  keywords={network science, graphs},
  url_Paper={http://arxiv.org/abs/1509.04037},
  abstract={Is the enemy of an enemy necessarily a friend? If not, to what extent
does this tend to hold? Such questions were formulated in terms of
signed (social) networks and necessary and sufficient conditions for a
network to be ‘balanced’ were obtained around 1960. Since then the idea
that signed networks tend over time to become more balanced has been
widely used in several application areas. However, investigation of this
hypothesis has been complicated by the lack of a standard measure of
partial balance, since complete balance is almost never achieved in
practice. We formalize the concept of a measure of partial balance,
discuss various measures, compare the measures on synthetic datasets and
investigate their axiomatic properties. The synthetic data involves
Erd\H{o}s-R\'{e}nyi and specially structured random graphs. We show that
some measures behave better than others in terms of axioms and ability
to differentiate between graphs. We also use well-known data sets from
the sociology and biology literature, such as Read's New Guinean tribes,
gene regulatory networks related to two organisms, and a network
involving senate bill co-sponsorship. Our results show that
substantially different levels of partial balance is observed under
cycle-based, eigenvalue-based and frustration-based measures. We make
some recommendations for measures to be used in future work.}
}

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