Community structure, a significant and useful statistical characteristic, is ubiquitous in social networks.17 Based on it, a network can be viewed as consisting of multiple units. The nodes (users) are highly connected to each other inside a unit, while the connections between units are sparse.4,17 For example, people with similar interests or backgrounds might join together to form a community or web-pages with related topics might cluster together. Different types of information, including rumors,5 virus attacks,10 and even cyber epidemics diffuse through social networks,8 possibly leading to unexpected social effects. A typical example is the worldwide cyberattack by WannaCry ransomware, as first reported May 12, 2017, that resulted in the infections of more than 200,000 organizations worldwide.15 The underlying attack reflects a malicious diffusion in the presence of communities; that is, the homogeneous feature of individuals leads to the community's vulnerability. It is against this back-drop that understanding the potential dynamics could help network administrators gain insight into controlling unwanted information diffusion. Much research today involves networks with community structure (such as to detect potential communities,21 model diffusion dynamics,6 and control information dissemination and sharing19). In particular, the influence of each node in the diffusion process must be taken into consideration. In simulation experiments, the source nodes that trigger diffusion are selected by researchers at random from a network or based on predefined measures of centrality.
In recent decades, multiple centrality measures have been proposed to statistically evaluate the importance or influence of a node (such as degree,2 betweenness,11 coreness,14 and eigenvector3). Degree is used mainly for characterizing the partial influence of a node.2 Betweenness reflects the potential power of a node in controlling information flow.11 Coreness implies that if a node lies in the core part of a network, the node is more important.14 And eigenvector accounts for two factors: a node's connections and its neighbors' influences.3 State-of-the-art studies have looked into nodes with relatively greater centrality in information diffusion. However, the influence of nodes with relatively less centrality on the diffusion process has never been completely addressed. In this article, we aim to explain the importance of two kinds of nodes in the information-diffusion process in a community-based network. Our findings can help network administrators better understand the diversity of communities and associated complexity of the diffusion process.