Leiden algorithm

The Leiden algorithm is an improvement on the Louvain algorithm for community detection, introduced by Traag, Waltman, and van Eck in 2019. Like Louvain, it greedily maximizes modularity through iterative local moves and network contraction. But Leiden adds a refinement phase after each contraction: communities are split into sub-communities that are guaranteed to be well-connected, and nodes are moved only to communities that improve modularity and maintain connectivity.

This refinement guarantees that all discovered communities are connected subgraphs — a property that the Louvain algorithm cannot ensure. The Leiden algorithm is therefore preferred in applications where community coherence matters, such as the analysis of biological networks and social networks where disconnected communities are semantically meaningless.