  The abundance of data about social relationships allows the human behavior to
be analyzed as any other natural phenomenon. Here we focus on balance theory,
stating that social actors tend to avoid establishing cycles with an odd number
of negative links. This statement, however, can be supported only after a
comparison with a benchmark. Since the existing ones disregard actors'
heterogeneity, we extend Exponential Random Graphs to signed networks with both
global and local constraints and employ them to assess the significance of
empirical unbalanced patterns. We find that the nature of balance crucially
depends on the null model: while homogeneous benchmarks favor the weak balance
theory, according to which only triangles with one negative link should be
under-represented, heterogeneous benchmarks favor the strong balance theory,
according to which also triangles with all negative links should be
under-represented. Biological networks, instead, display strong frustration
under any benchmark, confirming that structural balance inherently
characterizes social networks.
