A comprehensive multi-local-world model for complex networks

The nodes in a community within a network are much more connected to each other than to the others outside the community in the same network. This phenomenon has been commonly observed from many real-world networks, ranging from social to biological even to technical networks. Meanwhile, the number of communities in some real-world networks, such as the Internet and most social networks, are evolving with time. To model this kind of networks, the present Letter proposes a multi-local-world (MLW) model to capture and describe their essential topological properties. Based on the mean-field theory, the degree distribution of this model is obtained analytically, showing that the generated network has a novel topological feature as being not completely random nor completely scale-free but behaving somewhere between them. As a typical application, the MLW model is applied to characterize the Internet against some other models such as the BA, GBA, Fitness and HOT models, demonstrating the superiority of the new model.