American Journal of Mathematical and Computational Sciences  
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The Comparison of Entropy and Parameter Estimation in Complex Networks
American Journal of Mathematical and Computational Sciences
Vol.6 , No. 1, Publication Date: Jan. 22, 2021, Page: 1-5
2394 Views Since January 22, 2021, 563 Downloads Since Jan. 22, 2021

Zhao Chunxue, School of Mathematics and Statistics, Anyang Normal University, Anyang, China.


Entropy is used to describe the uniform distribution of any kind of energy in space. The more uniform the energy distribution, the higher the entropy. When the energy of a system is uniformly distributed, the entropy of the system reaches its maximum. Most complex systems can be described to network model, which includes a large number of nodes and complex connection relationships, Large number of networks show seemingly unrelated, but exist many striking similarities. According to different degree distribution, the network is divided into four kinds: regular network, random network, small-world network, scale-free network. Entropy is also a very important indicator which describes the heterogeneity of the networks. The scale-free network shows a non-homogeneous nature and a kind of sequence the complex network emerges. There have been some researches on using entropy to study complex networks. In the paper, we quantify the scale-free properties of the complex network by using the entropy theory and maximum likelihood estimation (MLE). We first review two kinds of entropy and prove their consistency; then we investigate the relationship of the parameter estimation among MLE, the moment estimator and the entropy of fitness scale-free network; finally, we gain the entropy of random network, which provides theoretical support for the practical application of entropy.


Complex Network, Entropy, Maximum Likelihood Estimation, Moment Estimator


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