Pinning controllability of complex networks with community structure

In this paper, we study the controllability of networks with different numbers of communities and various strengths of community structure. By means of simulations, we show that the degree descending pinning scheme performs best among several considered pinning schemes under a small number of pinned nodes, while the degree ascending pinning scheme is becoming more powerful by increasing the number of pinned nodes. It is found that increasing the number of communities or reducing the strength of community structure is beneficial for the enhancement of the controllability. Moreover, it is revealed that the pinning scheme with evenly distributed pinned nodes among communities outperforms other kinds of considered pinning schemes.