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：符号网络以边标为正或负为特征，能揭示超越无符号图所能实现的交互动态的细微洞察。其中核心任务是识别最大平衡子图，这对于社交网络中的极化社区检测和金融领域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，无法反映真实世界数据的复杂性。针对这一差距，我们引入了一种创新的广义平衡子图模型，该模型融入了对不规则性的容忍度。我们提出的基于区域的启发式算法专为此NP难问题设计，在低时间复杂度与高质量结果之间取得了平衡。对比实验验证了其相对于领先解决方案的卓越性能，在传统和广义场景下均实现了更高的有效性（特别是更大的子图规模）和效率（实现高达100倍的加速）。