Generating multi-scaling networks with different types of nodes

A variety of scale-free networks have been created since the pioneer work by A.-L. Barab\'{a}si and R. Albert. All this networks are homogeneous since they are composed of the same kind of nodes. In the realistic world, however, one element (node or vertex) in the network may play different roles and hence has different functions. In this Letter, we develop a new kind of network to account for this property. In our model, each type of nodes may exhibit a scaling law in the degree distribution and the scaling exponents are adjustable. As a consequence, the whole network lacks of such scaling characteristics, which indicates that many previous statistical results based on empirical data that claimed to be scale-free networks may need to be reexamined. This model poses an alternative way of the network division other than the module method. Besides, one can expect that this new network will exhibit some interesting properties concerning the dynamical processes on it.Comment: 4 figure