Stochastic Local Community Detection in Networks

We propose a stochastic agglomerative algorithm to detect the local community of some given seed vertex/vertices in a network. Instead of giving a deterministic binary local community in the output, our method assigns every vertex a value that is the probability that this particular vertex would be in the local community of the seed. The proposed procedure has several advantages over the existing deterministic algorithms, including avoiding random tie-breaking, evaluating uncertainties, detecting hierarchical community structure, etc. Synthetic and real data examples are included for illustration.