  Network is a simple but powerful representation of real-world complex
systems. Network community analysis has become an invaluable tool to explore
and reveal the internal organization of nodes. However, only a few methods were
directly designed for community-detection in directed networks. In this
article, we introduce the concept of local community structure in directed
networks and provide a generic criterion to describe a local community with two
properties. We further propose a stochastic optimization algorithm to rapidly
detect a local community, which allows for uncovering the directional modular
characteristics in directed networks. Numerical results show that the proposed
method can resolve detailed local communities with directional information and
provide more structural characteristics of directed networks than previous
methods.
