  We consider signed networks in which connections or edges can be either
positive (friendship, trust, alliance) or negative (dislike, distrust,
conflict). Early literature in graph theory theorized that such networks should
display "structural balance," meaning that certain configurations of positive
and negative edges are favored and others are disfavored. Here we propose two
measures of balance in signed networks based on the established notions of weak
and strong balance, and compare their performance on a range of tasks with each
other and with previously proposed measures. In particular, we ask whether
real-world signed networks are significantly balanced by these measures
compared to an appropriate null model, finding that indeed they are, by all the
measures studied. We also test our ability to predict unknown signs in
otherwise known networks by maximizing balance. In a series of cross-validation
tests we find that our measures are able to predict signs substantially better
than chance.
