Abstract
This paper investigates how to change the disassortativity of the whole network by connecting nodes of different types in two communities. A model connecting two multi-center networks is studied to see if analytical results are achievable. There are three main methods to connect two multi-center subnetworks depending on whether the connecting nodes are centers: (1) connect the centers of one sub-network to noncenter nodes of the other sub-network, (2) connect the centers of the two sub-networks together, and (3) connect non-center nodes of the two sub-networks. The results show that the disassortative property of a single multicenter network can be maintained in scenarios (1) and (2) above, but the disassortativity is changed in (3). In conclusion, either assortativity or disassortativity is achievable by connecting nodes with different degree properties in an ideal network constructed from two communities with similar network topology.
Highlights
The study of complex networks originated from the paper “Collective Dynamics of “Small World” Networks” 1 on Journal Nature 1998 by Watts and Strogatz, which unveils the small world effect
A lot of researches have been focused on the “scale-free” property of real-world networks, such as power-law degree distributions
It is known that complex networks have community structure, which brings up a natural question: how does the interconnection between communities affect the assortative property of the whole network? In general this kind of questions can only be solved by numerical method, but in this paper we will try to give analytical explanations
Summary
The study of complex networks originated from the paper “Collective Dynamics of “Small World” Networks” 1 on Journal Nature 1998 by Watts and Strogatz, which unveils the small world effect. Other aspects of complex networks including mechanism of epidemic spreading 3–6 , synchronization property 7–11 , cascading failure 12–14 have been studied Besides those generally acknowledged properties, mixing pattern is one of the important research subjects of complex networks as well. The characteristic property of nodes in a network preferentially connecting to those which are similar to themselves is called assortative mixing. The recent research on disassortativity is based on the following two main methods: 1 Assortativity coefficient r is the Pearson correlation coefficient of the degrees at either ends of an edge r. It is known that complex networks have community structure, which brings up a natural question: how does the interconnection between communities affect the assortative property of the whole network?
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