Research on cascading invulnerability of community structure networks under intentional-attack

In order to investigate the effects of community structure on cascading invulnerability,in the frame of a community structure network,the initial load of the node was defined by its betweenness,and the load on the broken node was redistributed to its neighboring nodes according to the preferential probability.When the node with the largest load being intentionally attacked in the network,the relation of load exponent,coupling-strength in a community,coupling-strength between communities,modularity function and the network's invulnerability were studied.The results show that the network's cascading invulnerability is positively related with coupling-strength in a community,coupling-strength between communities and modularity function,negatively related with load exponent.With comparison to BA (Barabási-Albert) scale-free network and WS (Watts-Strogatz) small-world networks,the result indicates that community structure lowers the network's cascading invulnerability,thus the more homogeneous betweenness distribution is,the stronger network's cascading invulnerability is.