With the small test graph we've used so far, the Label Propagation and Louvain algorithms yield the same communities, but this is not the case in general. The Zachary's karate club graph is a slightly larger graph and one of the most famous ones among graph experts. It was collected by Wayne W. Zachary, a teacher at the University of Chicago. He observed the different connections between the members of the karate club of this university in the 1970s.
The following image shows the result of Label Propagation (left) and the Louvain algorithm (right) on this graph, containing 34 nodes (students). While Label Propagation only captures two communities, the Louvain algorithm is able to detect four clusters:
Let me give you more context to understand this result better. In the karate club of the University of Chicago in around 1970, a conflict started between two instructors, which led to the...
