The effect of hub nodes on the community structure in scale-free networks

Many networks have two important features in common (1) the scale-free degree distribution P(k)∝k−α and (2) the community structure. In this paper, we focus on the relationship between these two features in complex networks. We first investigate the effect of the power law exponent α on the community structure in artificial networks and some real-world networks. Generally speaking, we find out that the networks with significant community structure, often have a large α. Second, hub nodes removal from scale-free networks affects the community structure more considerably than random removal. Our observation indicates that hubs may be the explanation for that scale-free networks often have fuzzy community structure.