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.

翻译：符号网络以边标记为正或负为特征，能够提供无符号图所无法捕捉的交互动态的细致洞察。其核心任务在于识别最大平衡子图，这对于社交网络中的极化社区检测和金融中的投资组合分析等应用至关重要。然而，传统模型受限于完美划分的假设，无法反映现实世界数据的复杂性。为弥补这一不足，我们提出了一种创新的广义平衡子图模型，该模型引入了对不规则性的容错机制。我们针对这一NP难问题设计的基于区域的启发式算法，在较低的时间复杂度与高质量结果之间取得了良好平衡。对比实验验证了其在传统及广义场景下均优于主流解决方案，展现出更高的有效性（特别是能发现更大的子图规模）和效率（最高可实现100倍的加速）。