%0 Journal Article
%T A Study on the Relationship between Connecting Different Types of Nodes and Disassortativity by Degree
%A Chengdong Dong
%J Mathematical Problems in Engineering
%D 2010
%I Hindawi Publishing Corporation
%R 10.1155/2010/891267
%X 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. 1. Introduction The study of complex networks originated from the paper ˇ°Collective Dynamics of ˇ°Small Worldˇ± Networksˇ± [1] on Journal Nature 1998 by Watts and Strogatz, which unveils the small world effect. Small-world networks exhibit both the highly clustered property as in regular lattices as well as having small characteristic path length as in random graphs. In 1999 Barabasi and Albert published the paper ˇ°Emergence of Scaling in Random Networksˇ± [2] in the journal Science. Because the emergence of scaling does not have apparent characteristic length, this type of networks is also called scale-free networks. Since then, a lot of researches have been focused on the ˇ°scale-freeˇ± property of real-world networks, such as power-law degree distributions. Subsequently, other aspects of complex networks including mechanism of epidemic spreading [3¨C6], synchronization property [7¨C11], cascading failure [12¨C14] have also 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. On the contrary, the phenomenon that nodes in a network preferentially connect to others unlike themselves most is called disassortative mixing. A lot of research shows that technological and biological networks generally possess disassortative characteristic while social networks usually possess assortative characteristic. In realistic applications [15], assortative networks (such as the social network of film
%U http://www.hindawi.com/journals/mpe/2010/891267/