Virus Spreading In Weighted Scale-free Networks With Community Structure

In recent years, an important discovery of complex networks is that many complex systems’degree distribution follows power-law degree distribution. Such complex networks includeInternet,WWW and metabolic network and so on. We call this kind of network scale-free network.Based on the scale-free network, there are many spreading behavior like the spreading ofcomputer virus in the Internet, the transmutation of a notice among crowds in a region and Theprevalence of infectious diseases in the crowd.With the further study scholars have found that alot of actual networks have a common characteristic-community structure where the links aredense in a community but sparse between communities. Now most of the researches on scale freenetworks with community structure have focused on unweighted networks. But the connection ofedges strength is heterogeneous:in the Internet, the flow size is different between any two routers,in aviation networks, the number of passengers is different in different lines. In this paper, westudy the spreading behavior of virus in weighted scale-free networks with community structure.First of all, we construct a modified weighted network with community structure inspired byBBV network model.Then theoretical derivation and simulation of the network’s topological characteristicsproved that the network’s degree distribution nodes strength distribution and edges weightdistribution all follow the power-law distribution so that the network can describe the realnetwork well.Finally, based on the proposed network, we use SI and SIR epidemic spreading model tostudy the influence of the weights parameter on the virus spreading and the results prove that alarger weights coefficient is helpful to control the epidemic spreading because it takes more timefor the virus from the source community of infection to spread to other communities when theweights coefficient is larger, the epidemic spreads quickly in unweighted networks. Besides wecontrast the influence of community strength on epidemic spreading and find that in the weightedscale-free networks a weaker community structure can help to control the epidemic spreadingwhile in the unweighted networks the results are diametrically opposite.