Epidemic spreading on complex networks with overlapping and non-overlapping community structure

• We propose a rewiring algorithm that changes the community structure from overlapping to non-overlapping while maintaining the degree distribution of the network.
• We simulate the susceptible-infected-susceptible (SIS) epidemic process on both synthetic scale-free networks and real-world networks.
• Experiments show that epidemics spread faster on networks with higher level of overlapping communities.
• Experiments show that the impact of community structure interacts with the impact of average degree of the network on epidemic spreading speed.

Many real-world networks exhibit community structure where vertices belong to one or more communities. Recent studies show that community structure plays an import role in epidemic spreading. In this paper, we investigate how the extent of overlap among communities affects epidemics. In order to experiment on the characteristic of overlapping communities, we propose a rewiring algorithm that can change the community structure from overlapping to non-overlapping while maintaining the degree distribution of the network. We simulate the Susceptible-Infected-Susceptible (SIS) epidemic process on synthetic scale-free networks and real-world networks by applying our rewiring algorithm. Experiments show that epidemics spread faster on networks with higher level of overlapping communities. Furthermore, overlapping communities’ effect interacts with the average degree’s effect. Our work further illustrates the important role of overlapping communities in the process of epidemic spreading.