Extracting principal parameters of complex networks

Yifang Ma () and Zhiming Zheng
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Yifang Ma: School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China;
Zhiming Zheng: LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, P. R. China

International Journal of Modern Physics C (IJMPC), 2015, vol. 26, issue 09, 1-11

Abstract: The evolution of networks or dynamic systems is controlled by many parameters in high-dimensional space, and it is crucial to extract the reduced and dominant ones in low-dimensional space. Here we consider the network ensemble, introduce a matrix resolvent scale function and apply it to a spectral approach to get the similarity relations between each pair of networks. The concept of Diffusion Maps is used to get the principal parameters, and we point out that the reduced dimensional principal parameters are captured by the low order eigenvectors of the diffusion matrix of the network ensemble. We validate our results by using two classical network ensembles and one dynamical network sequence via a cooperative Achlioptas growth process where an abrupt transition of the structures has been captured by our method. Our method provides a potential access to the pursuit of invisible control parameters of complex systems.

Keywords: Network ensemble; principal parameters; scale function; eigenvectors; 89.75.Hc; 83.85.Ns; 02.70.Hm (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S012918311550103X

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