This paper proposes LinkBlackHole', a novel algorithm for finding communities that are (i) overlapping in nodes and (ii) mixing (not separating clearly) in links. There has been a small body of work in each category, but this paper is the first one that addresses both. For this purpose, LinkBlackHole incorporates the advantages of both the link -space transformation and the black hole transformation. Thorough experiments show superior quality of the communities detected by LinkBlackHole* to those detected by other state-of-the-art algorithms.