Generating multi-scaling networks with different types of nodes

TL;DR

This paper introduces a new model for multi-scaling networks with different node types, allowing for adjustable degree distribution exponents, challenging the universality of scale-free network properties.

Contribution

It proposes a novel network model with multiple node types exhibiting individual scaling laws, expanding the understanding of complex network structures.

Findings

Networks can have heterogeneous scaling exponents for different node types

The overall network may not display scale-free properties despite individual node types doing so

The model offers an alternative to traditional module-based network division

Abstract

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.