A dynamical method to extract communities induced by low or middle-degree nodes

Many networks are proved to have community structure. Dense communities have been intensively investigated in recent years, oppositely seldom attention has been paid to sparse ones, which refer to those communities induced by low or middle-degree nodes rather than high-degree components. Recently, it has gradually been recognized that sparse community is also an important structure in biological networks because most disease genes and drug targets are within it. In this paper, we propose a dynamical method to extract sparse communities in complex networks by constructing local synchronization properties of phase oscillators. Compared to dense communities, sparse ones provide more general building and functional blocks in the networks without emphasis on the dominance of internal degrees over outside ones as well as the constraints of high degree connectors.