Obtaining Communities with a Fitness Growth Process

The study of community structure has been a hot topic of research over the last years. But, while successfully applied in several areas, the concept lacks of a general and precise notion. Facts like the hierarchical structure and heterogeneity of complex networks make it difficult to unify the idea of community and its evaluation. The global functional known as modularity is probably the most used technique in this area. Nevertheless, its limits have been deeply studied. Local techniques as the ones by Lancichinetti et al. and Palla et al. arose as an answer to the resolution limit and degeneracies that modularity has. Here we start from the algorithm by Lancichinetti et al. and propose a unique growth process for a fitness function that, while being local, finds a community partition that covers the whole network, updating the scale parameter dynamically. We test the quality of our results by using a set of benchmarks of heterogeneous graphs. We discuss alternative measures for evaluating the community structure and, in the light of them, infer possible explanations for the better performance of local methods compared to global ones in these cases.

💡 Research Summary

The paper tackles the long‑standing problem of community detection in complex networks by revisiting the local fitness‑maximization approach originally proposed by Lancichinetti et al. While global modularity‑based methods such as Louvain or Leiden are widely used, they suffer from a resolution limit and the existence of many near‑optimal partitions, which makes them unreliable on heterogeneous or hierarchical graphs. Local methods, on the other hand, evaluate the quality of a community from the perspective of its own internal and external connections, thereby avoiding the global resolution bias. However, the original Local Fitness Maximization (LFM) algorithm fixes the scale parameter α throughout the growth process, which limits its adaptability to regions of the network that have different densities or sizes.

To overcome this limitation, the authors introduce a dynamic scaling mechanism that updates α on‑the‑fly during community expansion. The fitness function remains
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