Detect local communities in networks with an outside rate coefficient

In this paper, we present a local method for detecting communities in networks. We define an outside rate coefficient _ψout${\psi }_{out}$ in our method. _ψout${\psi }_{out}$ has a very simple form and is easy to calculate. The local community enclosing a starting node can be detected by agglomerating the node with the smallest _ψout${\psi }_{out}$ at each time step. When there are two or more nodes having the same smallest outside rate coefficient _ψout${\psi }_{out}$, we agglomerate the node with the largest _kin$k_{in}$. This operation is remarkably beneficial to the accuracy of our method, and simulations on benchmark networks and real networks demonstrate that our local method is efficient to detect communities in networks.