Discovering Communities in Continuous-Time Temporal Networks by Optimizing L-Modularity

Abstract--Community detection is a fundamental problem in network analysis, with many applications in various fields. Extending community detection to the temporal setting with exact temporal accuracy, as required by real-world dynamic data, necessitates methods specifically adapted to the temporal nature of interactions. We introduce LAGO, a novel method for uncovering dynamic communities by greedy optimization of Longitudinal Modularity, a specific adaptation of Modularity for continuous-time networks. Unlike prior approaches that rely on time discretization or assume rigid community evolution, LAGO captures the precise moments when nodes enter and exit communities. We evaluate LAGO on synthetic benchmarks and real-world datasets, demonstrating its ability to efficiently uncover temporally and topologically coherent communities. Community detection is an important task in network analysis. It is used to uncover structural patterns and to reduce the complexity of large-scale graphs. Community detection has applications in many domains where systems can be modeled as networks, such as social science, economics, and biology. In the static setting, leading approaches such as Louvain [1], Infomap [2], or Leiden [3] typically rely on defining an objective function and optimizing it using greedy algorithms. This approach offers two main advantages: it produces communities that are meaningful according to a well-defined quality measure, and it scales efficiently to large graphs due to the computational simplicity of greedy methods. Real-world data often involves temporal dynamics, where interactions occur at specific timestamps.