In dynamic complex networks, entities interact and form network communities that evolve over time. Among the many static Community Detection (CD) solutions, the modularity-based Louvain, or Greedy Modularity Algorithm (GMA), is widely employed in real-world applications due to its intuitiveness and scalability. Nevertheless, addressing CD in dynamic graphs remains an open problem, since the evolution of the network connections may poison the identification of communities, which may be evolving at a slower pace. Hence, naively applying GMA to successive network snapshots may lead to temporal inconsistencies in the communities. Two evolutionary adaptations of GMA, sGMA and $\alpha$GMA, have been proposed to tackle this problem. Yet, evaluating the performance of these methods and understanding to which scenarios each one is better suited is challenging because of the lack of a comprehensive set of metrics and a consistent ground truth. To address these challenges, we propose (i) a benchmarking framework for evolutionary CD algorithms in dynamic networks and (ii) a generalised modularity-based approach (NeGMA). Our framework allows us to generate synthetic community-structured graphs and design evolving scenarios with nine basic graph transformations occurring at different rates. We evaluate performance through three metrics we define, i.e. Correctness, Delay, and Stability. Our findings reveal that $\alpha$GMA is well-suited for detecting intermittent transformations, but struggles with abrupt changes; sGMA achieves superior stability, but fails to detect emerging communities; and NeGMA appears a well-balanced solution, excelling in responsiveness and instantaneous transformations detection.

翻译：在动态复杂网络中，实体之间相互作用并形成随时间演化的网络社区。在众多静态社区检测解决方案中，基于模块度的Louvain算法（或称贪婪模块度算法，GMA）因其直观性和可扩展性而广泛应用于实际场景。然而，动态图中的社区检测仍是一个开放性问题——网络连接的演化可能干扰对社区结构的识别，而社区自身的演化速度可能相对较慢。因此，将GMA直接应用于连续的网络快照会导致社区在时间维度上的不一致性。针对该问题，研究者提出了两种GMA的进化变体：sGMA和$\alpha$GMA。但由于缺乏全面的评估指标和一致的真值基准，评估这些方法的性能并理解其各自适用场景成为一项挑战。为此，我们提出：(i) 一个面向动态网络中进化社区检测算法的基准测试框架；(ii) 一种广义模块度方法（NeGMA）。该框架可生成具有社区结构的合成图，并设计包含九种基本图变换且变换速率可调的演化场景。通过定义三项指标（正确性、延迟性、稳定性）进行性能评估，我们发现：$\alpha$GMA擅长检测间歇性变换，但难以应对突变；sGMA具有最优稳定性，但无法检测新出现的社区；而NeGMA展现出均衡性能，在响应速度和瞬时变换检测方面表现优异。