Distribution of node characteristics in complex networks of tree class

Authors:
Ying Tan;Hong Luo;Shou-Li Peng
Affiliations:
Center for Nonlinear Complex Systems, Department of Physics, Yunnan University, Kunming, China, Statistics and Mathematics College, Yunnan University of Finance and Economics, Kunming, China;School of Adult Education, Yunnan University, Kunming, China;Center for Nonlinear Complex Systems, Department of Physics, Yunnan University, Kunming, China
Venue:
AMT'12 Proceedings of the 8th international conference on Active Media Technology
Year:
2012

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Abstract

Based on the work of Park-Barabási (PB) we research in detail the (D, H)-phase diagram which describes the correlation and interplay among nodes of complex systems. To do this, we provide a frame of mathematical description, it includes: carrying out symbolization to the assortment of nodes, obtaining symbolic assertive matrix and enumeration formula. Applying the frame to two kinds of tree graphs we find that there exists vivid self-similar motif in the core domain of (D, H)-phase diagram. In order to draw the phase boundary we use a mixed curve of both Cassini oval and ellipse. The stationary of (D, H)-phase diagram is confirmed, but we also have seen a trend that the phase boundary has a phenomenon of little compression when the size of system increases. Finally, we suggest a new classification method to decide dyadic configuration of (D, H)-phase diagram and put it to use in the tree systems.