  Signed networks, characterized by edges labeled as either positive or
negative, offer nuanced insights into interaction dynamics beyond the
capabilities of unsigned graphs. Central to this is the task of identifying the
maximum balanced subgraph, crucial for applications like polarized community
detection in social networks and portfolio analysis in finance. Traditional
models, however, are limited by an assumption of perfect partitioning, which
fails to mirror the complexities of real-world data. Addressing this gap, we
introduce an innovative generalized balanced subgraph model that incorporates
tolerance for irregularities. Our proposed region-based heuristic algorithm,
tailored for this NP-hard problem, strikes a balance between low time
complexity and high-quality outcomes. Comparative experiments validate its
superior performance against leading solutions, delivering enhanced
effectiveness (notably larger subgraph sizes) and efficiency (achieving up to
100x speedup) in both traditional and generalized contexts.
