  Balance theory explains the forces behind the structure of social systems,
which are commonly modeled as static undirected signed networks. We expand this
modeling approach to incorporate directionality of edges, and consider three
levels of analysis: triads, subgroups, and the whole network. For triad-level
balance, we operationalize a new measure by utilizing semicycles that satisfy
the condition of transitivity. For subgroup-level balance, we propose measures
of cohesiveness (intra-group solidarity) and divisiveness (inter-group
antagonism) to capture balance within and among subgroups of the network using
the most fitting partition of nodes into two groups. For network-level balance,
we re-purpose the normalized line index to incorporate directionality, and
provide the proportion of edges whose position suits balance. Through extensive
computational analysis, we quantify and analyze patterns of social structure in
triads, subgroups, and the whole network across a range of social settings from
college students and Wikipedia editors to philosophers and Bitcoin traders. We
then apply our multilevel framework of analysis to examine balance in temporal
and multilayer networks, which demonstrates the generalizability of our
approach to evaluating balance, and leads to new observations on balance with
respect to time and layer dimensions. Our complementary findings on a variety
of social networks highlight the need to evaluate balance at different levels.
We propose a comprehensive yet parsimonious approach to address this need.
