Community discovery of complex networks,esp.of social networks,has been a hotly debated topic in academic circles in recent years.Since actual networks usually contain some overlapping nodes that are difficult to assign to a certain community,overlapping community discovery is under great demand in practical applications.However,at present network community discovery is mainly done by non-overlapping community discovery methods,overlapping discovery methods are not common.In this context,an overlapping community discovery method is proposed hereby based on topological potential and specific algorithms are also provided.This method not only considers the spread of the uncertainty of community identity of the overlapping nodes in the network,but also realizes a quantified representation,i.e.,uncertainty measure,of the community identity of the overlapping nodes.The experiment results show that this method yields the results that are consistent with those by the classic methods and are more reasonable.