Mixing local and global information for community detection in large networks

• We are investigating the emergence of a community structure in large online social networks such as Facebook.
• We propose a scalable method to maximize modularity in large networks.
• Our method uses global-level information but its scalability on large networks is comparable to that of local methods.
• Edge centralities were used to map network vertices onto points of a Euclidean space.
• Experiments on synthetic and real-world networks certify the accuracy of our method.

Clustering networks play a key role in many scientific fields, from Biology to Sociology and Computer Science. Some clustering approaches are called global because they exploit knowledge about the whole network topology. Vice versa, so-called local methods require only a partial knowledge of the network topology. Global approaches yield accurate results but do not scale well on large networks; local approaches, vice versa, are less accurate but computationally fast. We propose CONCLUDE (COmplex Network CLUster DEtection), a new clustering method that couples the accuracy of global approaches with the scalability of local methods. CONCLUDE generates random, non-backtracking walks of finite length to compute the importance of each edge in keeping the network connected, i.e., its edge centrality. Edge centralities allow for mapping vertices onto points of a Euclidean space and compute all-pairs distances between vertices; those distances are then used to partition the network into clusters.