  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\'enyi 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 datasets 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.
