Merging Complex Networks

In the cyber-physical society, networks are constructed for information transportation. Among them, power law networks with the scale free property are extensively found in self-organized systems. The dynamicity of the cyber-physical society drives large-scale networks keeping interacting and evolving. Several networks can be integrated or merged into one network during the evolving process of the whole cyber-physical society either because they share the same nodes or because one network is trying to connect to the other. A natural question is that in what way two or more networks will merge with each other so that their previous scale-free properties still hold. In this paper, we conducted a set of simulation experiments to study the effects of different merging processes on the degree distribution of merged networks. The result can be used to understand the merging process of complex networks in the cyber-physical society and also can be used to design an integration strategy for multiple networks.

I. Introduction

In the cyber-physical society [12], networks are extensively discovered or constructed in the natural physical space, the social space and the artificial spaces, and many phenomena can be also modelled as networks. Many natural and artificial networks are self-organized and developed with scale-free and small-world properties that make them scalable and efficient in information transportation [6] [11]. As the cyber-physical society evolves, various kinds of networks emerge and develop. Those networks who share nodes will finally meet each other as the messages are transferred between networks through shared nodes. In this process, nodes from different networks setup new links to evolve into a new network. Or, two networks begin to meet, interact, connect and finally merge each other. This process will keep going until the two networks reach a stable state in the topological aspect. Such process can happen after two separately developed networks begin to meet each other.